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Provide tags and a correct Python 3 solution for this coding contest problem. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is maximal. Greatest common divisor of sequence is ...
instruction
0
107,498
22
214,996
Tags: constructive algorithms, greedy, math Correct Solution: ``` ''' Hey why peeping here -_'_- ? I believe on myself and I will achieve this->author = Fuad Ashraful Mehmet, CSE ,University of Asia Pacific Todo: ''' import sys,math input=sys.stdin.readline def getSum(k): return k*(k-1)//2 def HalfDead(): ...
output
1
107,498
22
214,997
Provide tags and a correct Python 3 solution for this coding contest problem. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is maximal. Greatest common divisor of sequence is ...
instruction
0
107,499
22
214,998
Tags: constructive algorithms, greedy, math Correct Solution: ``` n,k = map(int,input().split()) if 2*n<k*(k+1): print(-1) exit(0) mx = 0 def ok(d): sm = k*(k-1)//2 sm *= d if sm+k>n: return False if (n-sm>((k-1)*d)): return True else: return False i = 1 while i*i<=n: if n%i==0: if ok(i): mx = max(mx,...
output
1
107,499
22
214,999
Provide tags and a correct Python 3 solution for this coding contest problem. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is maximal. Greatest common divisor of sequence is ...
instruction
0
107,500
22
215,000
Tags: constructive algorithms, greedy, math Correct Solution: ``` [n,k]=[int(x) for x in input().split()] m=k*(k+1)/2 limit=n//m lul="-1" def nice(x): global lul lul="" sum=0 a=[0]*k for i in range(1,k): a[i-1]=str(i*x) sum+=i*x a[k-1]=str(n-sum) print(" ".join(a)) pep=-1 f...
output
1
107,500
22
215,001
Provide tags and a correct Python 3 solution for this coding contest problem. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is maximal. Greatest common divisor of sequence is ...
instruction
0
107,501
22
215,002
Tags: constructive algorithms, greedy, math Correct Solution: ``` import math import sys array=list(map(int,input().split())) n = array[0] k = array[1] maxi = -1 for i in range(1, int(math.sqrt(n)) + 1): if n % i != 0: continue del1 = int(i) del2 = int(n / i) sum1 = del1 * k * (k - 1) / 2 sum2 = del2 * k * (k...
output
1
107,501
22
215,003
Provide tags and a correct Python 3 solution for this coding contest problem. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is maximal. Greatest common divisor of sequence is ...
instruction
0
107,502
22
215,004
Tags: constructive algorithms, greedy, math Correct Solution: ``` import sys #Library Info(ACL for Python/Pypy) -> https://github.com/not522/ac-library-python def input(): return sys.stdin.readline().rstrip() DXY = [(0, -1), (1,0), (0, 1), (-1,0)] #L,D,R,Uの順番 def divisors(n : int): res = [] for i in ran...
output
1
107,502
22
215,005
Provide tags and a correct Python 3 solution for this coding contest problem. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is maximal. Greatest common divisor of sequence is ...
instruction
0
107,503
22
215,006
Tags: constructive algorithms, greedy, math Correct Solution: ``` import sys #import random from bisect import bisect_left as lb from collections import deque #sys.setrecursionlimit(10**8) from queue import PriorityQueue as pq from math import * input_ = lambda: sys.stdin.readline().strip("\r\n") ii = lambda : int(inpu...
output
1
107,503
22
215,007
Provide tags and a correct Python 3 solution for this coding contest problem. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is maximal. Greatest common divisor of sequence is ...
instruction
0
107,504
22
215,008
Tags: constructive algorithms, greedy, math Correct Solution: ``` import math n, k = map(int, input().split()) if (k*(k+1))/2 > n: print(-1) else: c = int( n/ ((k*(k+1))/2)) a = [] for i in range(1, int( math.sqrt(n) + 1 ) ): if i*i == n: a.append(i) elif n%i == 0: ...
output
1
107,504
22
215,009
Provide tags and a correct Python 2 solution for this coding contest problem. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is maximal. Greatest common divisor of sequence is ...
instruction
0
107,505
22
215,010
Tags: constructive algorithms, greedy, math Correct Solution: ``` from sys import stdin, stdout from collections import Counter, defaultdict from itertools import permutations, combinations raw_input = stdin.readline pr = stdout.write def in_num(): return int(raw_input()) def in_arr(): return map(int,raw_in...
output
1
107,505
22
215,011
Provide tags and a correct Python 2 solution for this coding contest problem. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is maximal. Greatest common divisor of sequence is ...
instruction
0
107,506
22
215,012
Tags: constructive algorithms, greedy, math Correct Solution: ``` from sys import stdin, stdout from collections import Counter, defaultdict from itertools import permutations, combinations raw_input = stdin.readline pr = stdout.write def in_num(): return int(raw_input()) def in_arr(): return map(int,raw_in...
output
1
107,506
22
215,013
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is ma...
instruction
0
107,507
22
215,014
Yes
output
1
107,507
22
215,015
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is ma...
instruction
0
107,508
22
215,016
Yes
output
1
107,508
22
215,017
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is ma...
instruction
0
107,509
22
215,018
Yes
output
1
107,509
22
215,019
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is ma...
instruction
0
107,510
22
215,020
Yes
output
1
107,510
22
215,021
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is ma...
instruction
0
107,511
22
215,022
No
output
1
107,511
22
215,023
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is ma...
instruction
0
107,512
22
215,024
No
output
1
107,512
22
215,025
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is ma...
instruction
0
107,513
22
215,026
No
output
1
107,513
22
215,027
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is ma...
instruction
0
107,514
22
215,028
No
output
1
107,514
22
215,029
Provide tags and a correct Python 3 solution for this coding contest problem. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains four integers a,b,p,x (2 ≤ p ≤ 10^6+3, 1 ≤ a,b ...
instruction
0
107,562
22
215,124
Tags: chinese remainder theorem, math, number theory Correct Solution: ``` import sys ints = (int(x) for x in sys.stdin.read().split()) a,b,p,x = (next(ints) for i in range(4)) def ext_gcd(a, b): """return (g, x, y) such that a*x + b*y = g = gcd(a, b) and abs(x)<=b+1 ans abs(y)<=a+1""" x, x1, y, y1 = 0, 1, 1, 0 ...
output
1
107,562
22
215,125
Provide tags and a correct Python 3 solution for this coding contest problem. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains four integers a,b,p,x (2 ≤ p ≤ 10^6+3, 1 ≤ a,b ...
instruction
0
107,563
22
215,126
Tags: chinese remainder theorem, math, number theory Correct Solution: ``` import sys input = lambda : sys.stdin.readline().rstrip() sys.setrecursionlimit(2*10**5+10) write = lambda x: sys.stdout.write(x+"\n") debug = lambda x: sys.stderr.write(x+"\n") writef = lambda x: print("{:.12f}".format(x)) def gcd2(a, b): ...
output
1
107,563
22
215,127
Provide tags and a correct Python 3 solution for this coding contest problem. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains four integers a,b,p,x (2 ≤ p ≤ 10^6+3, 1 ≤ a,b ...
instruction
0
107,564
22
215,128
Tags: chinese remainder theorem, math, number theory Correct Solution: ``` import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = 'x' in file.mode...
output
1
107,564
22
215,129
Provide tags and a correct Python 3 solution for this coding contest problem. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains four integers a,b,p,x (2 ≤ p ≤ 10^6+3, 1 ≤ a,b ...
instruction
0
107,565
22
215,130
Tags: chinese remainder theorem, math, number theory Correct Solution: ``` a,b,p,x=map(int,input().split()) ans=0 for j in range(p-1): y=b*pow(pow(a,j,p),p-2,p)%p i=(j-y+p)%p t=i*(p-1)+j if(x-t>=0): ans+=((x-t)//(p*(p-1))+1) print(ans) ```
output
1
107,565
22
215,131
Provide tags and a correct Python 3 solution for this coding contest problem. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains four integers a,b,p,x (2 ≤ p ≤ 10^6+3, 1 ≤ a,b ...
instruction
0
107,566
22
215,132
Tags: chinese remainder theorem, math, number theory Correct Solution: ``` import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = 'x' in file.mode...
output
1
107,566
22
215,133
Provide tags and a correct Python 3 solution for this coding contest problem. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains four integers a,b,p,x (2 ≤ p ≤ 10^6+3, 1 ≤ a,b ...
instruction
0
107,567
22
215,134
Tags: chinese remainder theorem, math, number theory Correct Solution: ``` a,b,p,x = [int(x) for x in input().split()] ainv = pow(a,p-2,p) count = 0 n = 1 exp = ainv*b%p while n<p: m = n if exp>n: m += (n+p-exp)*(p-1) else: m += (n-exp)*(p-1) if m<=x: count += 1 + (x-m)//(p*(p-1)...
output
1
107,567
22
215,135
Provide tags and a correct Python 3 solution for this coding contest problem. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains four integers a,b,p,x (2 ≤ p ≤ 10^6+3, 1 ≤ a,b ...
instruction
0
107,568
22
215,136
Tags: chinese remainder theorem, math, number theory Correct Solution: ``` import os import sys from io import BytesIO, IOBase BUFSIZE = 8192 class FastIO(IOBase): newlines = 0 def __init__(self, file): self._fd = file.fileno() self.buffer = BytesIO() self.writable = 'x' in file.mode...
output
1
107,568
22
215,137
Provide tags and a correct Python 3 solution for this coding contest problem. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains four integers a,b,p,x (2 ≤ p ≤ 10^6+3, 1 ≤ a,b ...
instruction
0
107,569
22
215,138
Tags: chinese remainder theorem, math, number theory Correct Solution: ``` # import sys # sys.stdin = open('in.txt', 'r') a, b, p, x = map(int, input().split()) # A = [0, 1, 2, .. p-2, p-1] .. length = p # B = [1, a, a^2, .. a^(p-2)] .. length = p - 1 # x * inv(x) * b = b # a^x -> inv(a*x) * b #...
output
1
107,569
22
215,139
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains ...
instruction
0
107,570
22
215,140
Yes
output
1
107,570
22
215,141
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains ...
instruction
0
107,571
22
215,142
Yes
output
1
107,571
22
215,143
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains ...
instruction
0
107,572
22
215,144
Yes
output
1
107,572
22
215,145
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains ...
instruction
0
107,573
22
215,146
Yes
output
1
107,573
22
215,147
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains ...
instruction
0
107,574
22
215,148
No
output
1
107,574
22
215,149
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains ...
instruction
0
107,575
22
215,150
No
output
1
107,575
22
215,151
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains ...
instruction
0
107,576
22
215,152
No
output
1
107,576
22
215,153
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b (mod\;p), where a, b, p$$$ are all known constants. Input The only line contains ...
instruction
0
107,577
22
215,154
No
output
1
107,577
22
215,155
Provide a correct Python 3 solution for this coding contest problem. We have an integer sequence of length N: A_0,A_1,\cdots,A_{N-1}. Find the following sum (\mathrm{lcm}(a, b) denotes the least common multiple of a and b): * \sum_{i=0}^{N-2} \sum_{j=i+1}^{N-1} \mathrm{lcm}(A_i,A_j) Since the answer may be enormo...
instruction
0
107,660
22
215,320
"Correct Solution: ``` import sys readline = sys.stdin.readline ns = lambda: readline().rstrip() ni = lambda: int(readline().rstrip()) nm = lambda: map(int, readline().split()) nl = lambda: list(map(int, readline().split())) def primes(n): is_prime = [True] * (n + 1) is_prime[0] = is_prime[1] = False for...
output
1
107,660
22
215,321
Provide a correct Python 3 solution for this coding contest problem. A positive integer may be expressed as a sum of different prime numbers (primes), in one way or another. Given two positive integers n and k, you should count the number of ways to express n as a sum of k different primes. Here, two ways are consider...
instruction
0
107,813
22
215,626
"Correct Solution: ``` primes = [] flag = [0 for i in range(1121)] for i in range(2, 1121): if flag[i] == 0: primes.append(i) count = 2 while i * count < 1121: flag[i * count] = 1 count += 1 dp = [[0 for i in range(15)] for j in range(1121)] dp[0][0] = 1 for p in primes: for k...
output
1
107,813
22
215,627
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. A positive integer may be expressed as a sum of different prime numbers (primes), in one way or another. Given two positive integers n and k, you should count the number of ways to express n as ...
instruction
0
107,814
22
215,628
No
output
1
107,814
22
215,629
Provide a correct Python 3 solution for this coding contest problem. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq 10^4 * |a_i| \leq 10^9(0\leq i\leq N) * a_N \neq 0 * Al...
instruction
0
108,459
22
216,918
"Correct Solution: ``` def gcd(a, b): while b: a, b = b, a % b return a def prime_decomposition(n): i = 2 d = {} while i * i <= n: while n % i == 0: n //= i if i not in d: d[i] = 0 d[i] += 1 i += 1 if n > 1: if n not in d: d[n] = 1 return d def eratosthene...
output
1
108,459
22
216,919
Provide a correct Python 3 solution for this coding contest problem. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq 10^4 * |a_i| \leq 10^9(0\leq i\leq N) * a_N \neq 0 * Al...
instruction
0
108,460
22
216,920
"Correct Solution: ``` def gcd(a, b): a, b = max(a, b), min(a, b) while a % b > 0: a, b = b, a%b return b def divisor(a): i = 1 divset = set() while i * i <= a: if a % i == 0: divset |= {i, a//i} i += 1 divset.remove(1) return divset def is_prime(a): if a <=...
output
1
108,460
22
216,921
Provide a correct Python 3 solution for this coding contest problem. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq 10^4 * |a_i| \leq 10^9(0\leq i\leq N) * a_N \neq 0 * Al...
instruction
0
108,461
22
216,922
"Correct Solution: ``` def factorization(n): arr = [] temp = n for i in range(2, int(-(-n**0.5//1))+1): if temp%i==0: cnt=0 while temp%i==0: cnt+=1 temp //= i arr.append([i, cnt]) if temp!=1: arr.append([temp, 1]) ...
output
1
108,461
22
216,923
Provide a correct Python 3 solution for this coding contest problem. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq 10^4 * |a_i| \leq 10^9(0\leq i\leq N) * a_N \neq 0 * Al...
instruction
0
108,462
22
216,924
"Correct Solution: ``` def prime_fact(n: int)->list: '''n の素因数を返す ''' if n < 2: return [] d = 2 res = [] while n > 1 and d * d <= n: if n % d == 0: res.append(d) while n % d == 0: n //= d d += 1 if n > 1: # n が素数 res.a...
output
1
108,462
22
216,925
Provide a correct Python 3 solution for this coding contest problem. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq 10^4 * |a_i| \leq 10^9(0\leq i\leq N) * a_N \neq 0 * Al...
instruction
0
108,463
22
216,926
"Correct Solution: ``` import sys from fractions import gcd n = int(input()) a = [int(input()) for _ in range(n+1)] x = 0 while True: m = abs(sum([a[i]*pow(x, n-i) for i in range(n+1)])) if m != 0: break x += 1 ps = [] i = 2 while i**2 <= m and i <= n+1: #for i in range(2, int(sqrt(m))+1): if m%i == 0: ps.appe...
output
1
108,463
22
216,927
Provide a correct Python 3 solution for this coding contest problem. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq 10^4 * |a_i| \leq 10^9(0\leq i\leq N) * a_N \neq 0 * Al...
instruction
0
108,464
22
216,928
"Correct Solution: ``` from functools import reduce import random MOD = 59490679579998635868564022242503445659680322440679327938309703916140405638383434744833220555452130558140772894046169700747186409941317550665821619479140098743288335106272856533978719769677794737287419461899922456614256826709727133515885581878614846...
output
1
108,464
22
216,929
Provide a correct Python 3 solution for this coding contest problem. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq 10^4 * |a_i| \leq 10^9(0\leq i\leq N) * a_N \neq 0 * Al...
instruction
0
108,465
22
216,930
"Correct Solution: ``` import sys from fractions import gcd n = int(input()) a = [int(input()) for _ in range(n+1)] x = 0 while True: m = abs(sum([a[i]*pow(x, n-i) for i in range(n+1)])) if m != 0: break x += 1 ps = [] i = 2 while i**2 <= m and i <= n+1: if m%i == 0: ps.append(i) while m%i == 0: m //= i ...
output
1
108,465
22
216,931
Provide a correct Python 3 solution for this coding contest problem. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq 10^4 * |a_i| \leq 10^9(0\leq i\leq N) * a_N \neq 0 * Al...
instruction
0
108,466
22
216,932
"Correct Solution: ``` def factors(z): ret = [] for i in range(2, int(z**(1/2))+1): if z%i == 0: ret.append(i) while z%i == 0: z //= i if z != 1: ret.append(z) return ret def eratosthenes(N): if N == 0: return [] from collections i...
output
1
108,466
22
216,933
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq...
instruction
0
108,467
22
216,934
Yes
output
1
108,467
22
216,935
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq...
instruction
0
108,468
22
216,936
Yes
output
1
108,468
22
216,937
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq...
instruction
0
108,469
22
216,938
Yes
output
1
108,469
22
216,939
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq...
instruction
0
108,470
22
216,940
Yes
output
1
108,470
22
216,941
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq...
instruction
0
108,471
22
216,942
No
output
1
108,471
22
216,943
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response. You are given a polynomial of degree N with integer coefficients: f(x)=a_Nx^N+a_{N-1}x^{N-1}+...+a_0. Find all prime numbers p that divide f(x) for every integer x. Constraints * 0 \leq N \leq...
instruction
0
108,472
22
216,944
No
output
1
108,472
22
216,945