A workshop has n parts, each with a positive integer load, and k benches. The foreman wants to distribute every part to some bench so that each of the k benches ends up with exactly the same total load, and every bench receives at least one part.
Determine whether such a distribution is possible.
Input format
Line 1: two integers n and k.
Line 2: n space-separated positive integers, the part loads.
Output format
Print YES if the parts can be split into k equal-load groups, otherwise NO.
Constraints
- 1 <= n <= 12
- 1 <= k <= 6
- 1 <= each load <= 50