Time Limit: 2000 MS    Memory Limit: 65536 K 


Description

The definition of Reducible Array {A0, A1, A2, бн, AN-1} can be showed as follow: 1. An array {Ax} consisting of only one element cannot be reduced, and Ax is the target. 2. Otherwise, any element Ai ( 0 <= i <= N-2 ) of the array {A0, A1, A2, бн, AN-1} can be reduced to a smaller array by replacing Ai and Ai+1 with the subtraction of Ai and Ai+1, namely Ai-Ai+1. For example, the procedure that {12, 10, 4, 3, 5} reduces to {4}, the target, can be illustrated as: {12, 10, 4, 3, 5} {12, 6, 3, 5} {12, 6, -2} {12, 8} {4} Obviously, there are many different targets of a Reducible Array, varying according to different orders the reducing procedures adopted. Now, Rain want to know whether there is such an order that, if the reducing procedure is adopted, would result in a given target M.

Input

The first line of input is the number of test case. For each test case: The first line contains two integers N and M. The second line contains N integers. There is a blank line before each test case. 3 <= N <= 20 -231 <= M <= 231-1 -108 <= Ai <= 108

Output

For each test case output the answer on a single line: "Yes" or "No".

Sample Input

2 5 4 12 10 4 3 5 5 7 12 10 4 3 5

Sample Output

Yes No

Source

8th SCUPC

Author

windy7926778