| 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: | |
|  | |