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Circular tour
     

Consider circular track with n points marked as 1, 2, …n. A person is initially placed on point k. The person moves m > 0, slot forward (in circular way) in each step. Find the minimum number of steps required so that the person reaches initial point k.

Input:
The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. Each test case contains integers n,k,m.

Output:
Print the minimum number of steps required so that the person reaches initial point k.

Constraints:
1<=T<=10^5
1<=n<=10^5
1<=m<=10^5
1<=k<=n

Example:
Input:

2
9 2 6
6 3 2

Output:
3
3

Explanation: In the first test case, Sequence of moves is 2 => 8 => 5 => 2.So total number of moves are 3.

** For More Input/Output Examples Use 'Expected Output' option **

Contributor: Ayush Govil

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