You are given an array Arr containing N numbers and an integer K. You can implement the following operations on this array:

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

You cannot perform more than one operation per element of the array.

Write a program to determine whether it is possible to make the sum of all the elements in the array Arr equal to K.

Input format

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

Output format

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

Constraints

\(1 ≤ T ≤ 50\)
\(1 ≤ N ≤ 100\)
\(1 ≤ K ≤ 10000\)
\(0 ≤ Arr_i ≤ 100\)