Alternating Work Days Problem Code: ALTER Answer

October Lunchtime 2021 Division 3 » Alternating Work Days

Alternating Work Days Problem Code: ALTER

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Alice and Bob are two friends. Initially, the skill levels of them are zero. They work on alternative days, i.e one of Alice and Bob works on the odd-numbered days(1,3,5,…) and the other works on the even-numbered days (2,4,6,…). The skill levels of Alice and Bob increase by A,B respectively on the days they work.

Determine if it is possible that the skill levels of Alice and Bob become exactly P,Q respectively on some day.

Input Format

The first line contains an integer T, denoting the number of test cases. The T test cases then follow:

The first and only line of each test case contains four space-separated integers A,B,P,Q.

Output Format

For each test case, print YES if it is possible that the skill levels of Alice and Bob become exactly P,Q on someday, otherwise print NO.

You may print each character of the string in uppercase or lowercase (for example, the strings "yEs", "yes", "Yes" and "YES" will all be treated as identical).

Constraints

1≤T≤103

1≤A,B,P,Q≤109

Subtasks

Subtask 1 (100 points): Original constraints

Sample Input 1

1 2 1 2

1 2 3 2

4 3 4 6

3 5 9 25

Sample Output 1

YES

Explanation

Test Case 1: Alice works on the first day and gains skill level 1. Bob works on the second day and gains skill level 2.

Test Case 2: There is no possible way that the skill levels of Alice and Bob become 3 and 2 respectively.

Test Case 3: Bob works on the first and third day and Alice works on the second day. Hence after the third day, the skill levels of Alice and Bob become 1⋅4=4 and 2⋅3=6 respectively.