# 1035. Comfort

A game-board consists of N fields placed around a circle. Fields are successively numbered from1 to N clockwise. In some fields there may be obstacles.

Player starts on a field marked with number 1. His goal is to reach a given field marked with number Z. The only way of moving is a clockwise jump of length K. The only restriction is that the fields the player may jump to should not contain any obstacle.

For example, if N = 13, K = 3 and Z = 9, the player can jump across the fields 1, 4, 7, 10, 13, 3, 6 and 9, reaching his goal under condition that none of these fields is occupied by an obstacle.

Your task is to write a program that finds the smallest possible number K.

### 输入格式

It contains multi-testcases.(**** Please notice that it has more than one test case and please use While(scanf()!=EOF) just as problem 1000)

First line of the each testcase consists of integers N, Z and M, 2 <= N <= 1000, 2 <= Z <= N, 0 <= M <= N - 2. N represents number of fields on the game-board and Z is a given goal-field.

Next line consists of M different integers that represent marks of fields having an obstacle. It is confirmed that fields marked 1 and Z do not contain an obstacle.

### 输出格式

For each testcase output a line contains the requested number K described above.

### 样例

Input
9 7 2
2 3
9 7 2
2 3

Output
3
3


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