Kindness

Limits: 2 sec., 256 MiB

"Today is a very good day" — thought Zenyk and decided to give out candies to all children. Zenyk has \(N\) boxes with candies, \(i\)-th box contains \(A_i\) candies, all boxes are placed in a row.

Zenyk met \(K\) children. Every child get some continuous subarray of boxes. More formally Zenyk chooses 2 integers \(L\), \(R\) and presents \(A_L+A_{L+1}+\dots+A_R\) candies. After that \(L-1\)-th and \(R+1\)-th boxes become neighboring.

You should find if Zenyk can giveaway all boxes such that every child get the same amount of candies.

Input

First line contains 2 integers \(N\) and \(K\).

Second line contains \(N\) integers \(A_i\).

Output

Print "YES" if Zenyk can giveaway all candies and "NO" otherwise.

Constraints

\(1 \le N \le 500\),

\(1 \le K \le N\),

\(1 \le A_i \le 10^9\).

Samples

Input (stdin) сopy	Output (stdout) сopy
4 2 2 3 4 5	YES

Input (stdin) сopy	Output (stdout) сopy
4 2 2 3 5 4	NO

Notes

In the first sample Zenyk gives 2-nd and 3-rd boxes to the first child. Then remaining 2 boxes (2,5) to the second child. Both children get 7 candies.