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.