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2231.   Super A+B Problem
Time Limit: 2.0 Seconds   Memory Limit: 65536K
Total Runs: 3520   Accepted Runs: 1122

The A+B Problem seems a little easy, now we turn to an enhanced version...

Given a series of numbers, your task is to pick up some numbers, so that the sum of these numbers is a given S.

Input

The first line of each test contains the amount of the numbers N (1 ≤ N ≤ 20), and the sum S. Then N integers followed in the second line seperated by spaces. You can assume the sum S and all the N numbers are in the range [-10000, 10000].

The input is terminated by a line with N = S = 0.

Output

Output one line for each test case. If you can pick up some numbers whose sum is S, just output "Yes". Otherwise, output "No".

Sample Input

3 4
1 2 3
4 10
1 2 3 -4
0 0


Sample Output

Yes
No


Author: RoBa

Source: TOJ 2006 Weekly Contest 6
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