There is a sequence of integer numbers A₁, A₂, …, 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:

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 "YES", if the mentioned above inequality holds for all the values of the parameters i and j, and "NO" otherwise.