Given four integers A, B, C, D. A represents the initial position of the geek on the x-axis. In each step, geek can go to X+B or X-B if he is standing at X. The tasks is to check if it is possible for the geek to reach C exactly after D steps.

Input:
1. The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
2. The first line of each test case contains four space-separated integers A, B, C, and D.

Output: For each test case, print "yes" if it is possible to reach C in exactly D steps. Otherwise, print "no" (without quotes).

Constraints:
1. 1 <= T <= 5
2. -10^9 <= A, C <= 10^9
3. 1 <= B <= 10^9
4. 1 <= D <= 15

Example:
Input:
3
2 3 8 4
-3 1 0 3
-3 1 1 3

Output:
yes
yes
no

Explanation:
Test case 1: one of the possible ways is {2, 5, 8, 11, 8}.