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50837 - Sum is equal to K

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Time limit 2000/4000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.
Question by Ibrahim Mesecan.

Sum is equal to K

Math professor of your brother gave a homework for kids. The professor gives n numbers, and he asks if number k can be produced by adding or subtracting any given number.

Question: Write a program that is going to get information and decide if it's possible to calculate the given number k or not.

Input specification
In the first line, you will be given two integers: The number of numbers(n) and the number (k) to calculate where 0 ≤ n ≤ 17 and -20,000 ≤ k ≤ 20,000. Then, in the following line, you will be given n integers where each number is between -10,000 and 10,000.

Output specification:
Show "No", if it is not possible to calculate k. Otherwise, show "Yes" in the first line. Then, in the next line show the numbers whose sum is equal to k.
Note:

  1. Each input number can be used only once.
  2. There can be many possible solutions. It is OK to show any correct solution.

Sample Input I
4 7
1 2 3 5
Sample Input II
4 8
1 2 3 10
Sample Output I
Yes
2 5
Sample Output II
Yes
-2 10



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