Given a circular array  of length and a positive integer , you can perform the following operation any number of times (including zero):

• Select two indices  and  () such that , which means the minimum distance between  and  on the circular array is , and subtract  from both  and .

Determine if it is possible to transform the entire array into . If possible, output YES; otherwise, output NO. 

You are given  test cases. Find the answer for each of them.

输入描述:

The first line contains a positive integer  () , denoting the number of test cases. The first line of each test case contains two positive integers  and  (, ), indicating the length of the array  and the minimum distance of  and  for each index selection. The second line consists of  non-negative integers  ().
It is guaranteed that .

输出描述:

For each test case, output one string per line, either "YES" or "NO" (without quotes), indicating whether it is possible or not.

5
5 2
3 0 5 1 3
6 3
5 0 0 3 0 0
5 5
1 2 3 4 5
6 1
0 0 1 0 0 1
7 2
1 1 0 1 1 1 1

YES
NO
NO
NO
YES

For the first test case, perform these operations: .
For the third test case, you can't do any operation, so it's impossible to transform the entire array into .