An array A of N integers is said to special if we can obtain the total sum of the array as K by the implementation of the following operation:

• Replace an element A[i] with A[i] + i
• Replace an element A[i] with -A[i]
• Replace an element A[i] with A[i] - i

Note: You can only perform one operation per element of the array.

If it is possible to make the sum of the array A equal to K i.e Special Array, print YES else NO.

Input format

• First line: T (number of test cases)
• First-line in each test case: Two space-separated integers N and K
• The second line in each test case: N space-separated integers (denoting the array A)

Output format

For each test case, print YES or NO depending on the result.

Constraints

• 1 ≤ T ≤ 50
• 1 ≤ N ≤ 100
• 1 ≤ K ≤ 10000
• 0 ≤ A[i] ≤ 100