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A Modular Arithmetic Challenge
Time Limit: 1000MSMemory Limit: 131072K
Total Submissions: 1877Accepted: 270

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.

Sample Input

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

Sample Output

3
-1
1
-1

Source

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