A relay squad wants to divide n tokens into exactly K hoards so that every hoard has the same total value. Each token has a positive whole-number value and must go into exactly one hoard; because every value is positive and each hoard must reach the common total, no hoard can be empty. Decide whether such a split into K equal-value hoards is possible.
Input format
Line 1: two integers n and K.
Line 2: n space-separated positive integers, the token values.
Output format
Print YES if the tokens can be partitioned into exactly K groups of equal total value, otherwise NO.
Constraints
- 1 <= K <= n <= 16
- 1 <= each value <= 1000