Mr. Seth provides you a sequence of integers a₁, a₂, ..., a_n. Your task is to find whether you can make the sequence as K divisible sequence by adding d as many times as you require until a[i] <= 2*10⁴.

Note: A K divisible sequence is the sequence of integers where each integer is divisible by K.

Example -

N=5, K=2, and d=1
Sequence: 1 2 3 4 5

So you can make this sequence K divisible sequence just by adding d 1 time in elements 1,3 and 5 of the given sequence.

Input

The first line of the input contains an integer T describing the number of test cases.
The first line of T test cases contains three space-separated integers N, K, and D.
The last line of the test case contains N space-separated integers.

Output

Print 'YES' if it is possible to make sequence K divisible else 'NO' in each test case.

Constraints

1 <= T <= 10
1 <= N,K,D <= 100
1 <= A [i]<= 1000