| Carlos knows that the key to sustained customer loyalty is early customer |
| acquisition and constant re-engagement. With that in mind, he's setting his |
| sights on sugary cereals. Kids love it, and they keep coming back for more. He |
| has a proposal for Post, the well-known manufacturer of Alpha-Bits: |
|
|
| _ "For 60 years these bits have been made of letters, but kids today are tired |
| of letters for breakfast. Let me show you something truly revolutionary: bits |
| made of numbers!" _ |
|
|
| The executives at Post would like to assess the feasibility of producing |
| numeric bits. In particular, they want to see if Carlos can create a string of |
| bits, **B**, of length **N**. In this string, each character is either `'0'` |
| or `'1'`. |
|
|
| Carlos has been given a list of **M** requirements. The _i_th requirement |
| states that the substring **BXi...Yi** must be a palindrome. The new cereal |
| surely won't succeed without appealing to children's acute sense of symmetry. |
|
|
| Furthermore, the number of zeroes and ones in **B** must be as close as |
| possible. In other words, if `C(b)` is the number of occurrences of bit _b_ in |
| **B**, then the absolute difference `|C(0) - C(1)|` must be minimized. The |
| margins on cereal are razor thin, and as everybody knows, bits are produced in |
| pairs, so it's wasteful to use more of one sort than the other. |
|
|
| Help Carlos build any bitstring **B** consistent with all of these |
| requirements (and with minimal difference between the number of zeroes and |
| ones). It's guaranteed that such a bitstring exists for every given set of |
| requirements. |
|
|
| ### Input |
|
|
| Input begins with an integer **T**, the number of bitstrings that Post has |
| commissioned. For each bitstring, there is first a line containing the space- |
| separated integers **N** and **M**. Then, **M** lines follow, the _i_th of |
| which contains the space-separated integers **Xi** and **Yi**. |
|
|
| ### Output |
|
|
| For the _i_th commission, print a line containing "Case #_i_: " followed by a |
| valid bitstring **B**. |
|
|
| ### Constraints |
|
|
| 1 ≤ **T** ≤ 350 |
| 1 ≤ **N** ≤ 4,000 |
| 0 ≤ **M** ≤ 10,000 |
| 1 ≤ **Xi** ≤ **Yi** ≤ **N** |
|
|
| ### Explanation of Sample |
|
|
| In the first case, the minimum absolute difference between the number of |
| zeroes and ones is 0 (with 2 of each). **5 other outputs would also be |
| accepted** for this case: "0011", "0101", "0110", "1001", and "1010". **For |
| each of the remaining sample cases, various other outputs would similarly be |
| accepted.** |
|
|
| In the second case, the minimum achievable difference is 2. |
|
|
| In the third case, the minimum achievable difference is 2. |
|
|
| In the fourth case, the minimum achievable difference is 1. |
|
|
| In the fifth case, the minimum achievable difference is 0. |
|
|
| In the sixth case, the minimum achievable difference is 9. |
|
|
|
|
