| Fred works the night shift in a refrigerator storage warehouse. It's not very |
| exciting work, but Fred has ways to pass the time when nobody's around. For |
| example, lifting fridges turns out to be an amazing bodybuilding method! |
|
|
| The warehouse consists of **N** sections in a row, numbered from 1 to **N**. |
| In each section _i_, there are initially **Fi** fridges, all arranged in a |
| single stack. The sections are intended to be separate from one another, and |
| only accessible from the outside. To that end, each pair of adjacent sections |
| are separated by a wall, for a total of **N**-1 walls. However, these walls |
| don't stretch all the way to the ceiling, and aren't necessarily all of the |
| same height. The wall between sections _i_ and _i_+1 has a height of **Hi** |
| fridge-heights (Fred has come to measure everything relative to fridge |
| dimensions). Fred's favourite pastime involves climbing over these walls to |
| get between the warehouse's sections! |
|
|
| Fred will begin by entering the warehouse in some section, carrying in some |
| number of new fridges from the outside (yes, he's become strong enough to |
| carry multiple fridges in his arms at once). When he's currently in a certain |
| section _s_ and is carrying _f_ fridges, he may perform any of the following |
| actions: |
|
|
| * Pick up a fridge from section _s_'s stack of fridges, if it's non-empty. This decreases the number of fridges in that stack by 1, and increases _f_ by 1. |
| * Add a fridge that he's carrying onto section _s_'s stack of fridges, if he's carrying at least one fridge. This decreases _f_ by 1, and increases the number of fridges in that stack by 1. |
| * Climb onto section _s_'s stack of fridges and jump over a wall into an adjacent section, if the number of fridges in that stack is at least as large as the height of that wall (in fridge-heights). This decreases or increases _s_ by 1. |
|
|
| Fred's goal is to visit all **N** sections at least once each. He just needs |
| to decide which section he should initially enter and how many additional |
| fridges he should bring from the outside. He has **M** such possible starting |
| situations in mind, the _i_th of which involves him beginning in section |
| **Xi** while carrying **Yi** fridges. For each hypothetical starting |
| situation, please help Fred determine whether or not he will be able to visit |
| all **N** sections! |
|
|
| ### Input |
|
|
| Input begins with an integer **T**, the number of warehouses Fred works at. |
| For each warehouse, there is first a line containing the space-separated |
| integers **N** and **M**. |
| Then follows a line with the **N** space-separated integers **F1** through |
| **FN**. |
| Then follows a line with the **N** \- 1 space-separated integers **H1** |
| through **HN-1**. |
| Then, **M** lines follow, the _i_th of which contains the space-separated |
| integers **Xi** and **Yi**. |
|
|
| ### Output |
|
|
| For the _i_th warehouse, print a line containing "Case #_i_: " followed by a |
| string of **M** characters, the _i_th of which is "Y" if Fred can visit all |
| **N** sections from the _i_th starting situation, or "N" otherwise. |
|
|
| ### Constraints |
|
|
| 1 ≤ **T** ≤ 90 |
| 2 ≤ **N** ≤ 8,000 |
| 1 ≤ **M** ≤ 8,000 |
| 0 ≤ **Fi** ≤ 100,000 |
| 1 ≤ **Hi** ≤ 100,000 |
| 1 ≤ **Xi** ≤ **N** |
| 0 ≤ **Yi** ≤ 1,000,000,000 |
|
|
| The sum of **N** across all **T** test cases is no greater than 80,000. |
| The sum of **M** across all **T** test cases is no greater than 80,000. |
|
|
| ### Explanation of Sample |
|
|
| In the first case, the warehouse is arranged as follows: |
|
|
|  |
|
|
| If Fred begins in section 1 holding 0 fridges, he can't climb over the wall to |
| visit section 2, whereas if he's holding 1 fridge, he can place it in section |
| 1 and then climb over. On the other hand, if he begins in section 2, he can |
| climb over the wall to visit section 1 using the existing fridge, regardless |
| of whether he's holding any himself. |
|
|
| In the second case, consider the first starting situation, in which Fred |
| begins in section 3 holding 4 fridges: |
|
|
|  |
|
|
| He could begin by placing 3 of his fridges in section 3, and using them to |
| climb over the wall into section 4 while still holding 1 fridge: |
|
|
|  |
|
|
| He could then place his remaining fridge in section 4, climb back to section |
| 3, pick up a fridge there, and climb over to section 2 while holding that 1 |
| fridge: |
|
|
|  |
|
|
| Finally, he could place his final fridge in section 2 and climb over to |
| section 1: |
|
|
|  |
|
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|
