Description

Given four positive integers M, D, L, R, your task is to find the minimal non-negative integer x which satisfies L ≤ ( D × x mod M ) ≤ R, where mod is the remainder operation

Input

The first line contains one number N -- the number of test cases.(1 ≤ N ≤ 100)
Each of the following N lines contains four integers M, D, L, R ( 1≤ M, D, L, R ≤ 2,000,000,000)

Output

For each test case, print the minimal x. If there is no such x, print "-1" instead.

4
4 3 1 1
4 2 1 1
4 2 2 4
4 4 4 4

3
-1
1
-1

Source

POJ Founder Monthly Contest – 2008.03.16, Gao Yihan