| Aliens on the Unknown planet have a tradition of playing a game called Loiten. | |
| It is played by two players who alternate turns. There are **N** buckets with | |
| apples standing in one line in front of the players. They are numbered from | |
| left to right with integers starting from 1. | |
| In one turn a player can select one of the buckets, which is not the first and | |
| not the last and has a positive number of apples in it, and move all of that | |
| bucket's apples to the bucket adjacent to the left and at the same time move | |
| all of them to the bucket adjacent to the right. That's right, the number of | |
| apples can be negative as it is a really strange planet. Thus, if there are 3 | |
| consecutive buckets with the number of apples being **x**, **y**, **z**, then | |
| you can perform the move if **y** is greater than zero. The resulting capacity | |
| of the buckets will be as follows: **x+y**, **-y**, **z+y**. The first player | |
| who can't make a move loses. | |
| You happen to know one of the aliens from the Unknown planet, named Popo. He | |
| is a very good Loiten player, and has reached the Loiten Finals. On the day | |
| prior to the game, he found out the number of apples in each of the buckets. | |
| Unfortunately, his memory is not that good, and he can't remember the number | |
| of apples in the **P**-th bucket. He just remembers that it is a number with | |
| absolute value not greater than **F**. | |
| Now, he is asking you to help him to calculate his chances. The players at the | |
| Finals are so good that they only make optimal moves to maximize their chance | |
| of winning. If neither player can win, the game is considered a draw. You are | |
| to find the number of possible apple counts for the bucket with an unknown | |
| number of apples where Popo will win. Popo is also sure that he is the one to | |
| make the first turn. | |
| ## Input | |
| The first line of the input file consists of a single number **T**, the number | |
| of test cases. Each test case begins with a line containing two integers | |
| **N**, the number of buckets and **P**, the number of the bucket with the | |
| unknown amount of apples. It is followed by a line containing **N** integers, | |
| the numbers of apples in the corresponding buckets. The **P**th number on this | |
| line is the positive integer **F** and corresponds to the constraint on the | |
| number of apples in the **P**-th bucket. | |
| ## Output | |
| Output **T** lines, with the answer to each test case on a single line, the | |
| number of possible values for unknown bucket. | |
| ## Constraints | |
| **T** = 50 | |
| 1≤ **P** ≤ **N** ≤ 2,000. | |
| 1≤ **F** ≤ 1,000,000,000,000. | |
| The number of apples in each bucket at the start of the game has an absolute | |
| value not greater than 1,000,000,000,000. | |