There is a sequence of integer numbers A_{1}, A_{2}, …, A_{S}, and a positive integer N. It's known that all elements of the sequence {A_{i}} satisfy the restriction 0 ≤ A_{i} ≤ 100. Moreover, it's known that the sum of all elements of the sequence is equal to S + N. You are to write a program that given a sequence {A_{i}} and a number N will answer the question: is it true that for all 1 ≤ i ≤ j ≤ S the following inequality holds:
A_{i} + A_{i+1} + … + A_{j} ≤ (j – i + 1) + N ?
Input
The first input line contains two separated with a space positive numbers S and N that do not exceed 30000. Then follow S lines with one number in a line that are elements of the sequence {A_{i}}.
Output
Output "YES", if the mentioned above inequality holds for all the values of the parameters i and j, and "NO" otherwise.
Samples
input  output 

4 3
2
3
0
2
 YES

4 5
1
0
5
3
 NO

Problem Author: Alexander Mironenko
Problem Source: Ural State University Personal Programming Contest, March 1, 2003