ENG  RUSTimus Online Judge
Online Judge
Problems
Authors
Online contests
About Online Judge
Frequently asked questions
Site news
Webboard
Links
Problem set
Submit solution
Judge status
Guide
Register
Update your info
Authors ranklist
Current contest
Scheduled contests
Past contests
Rules

1247. Check a Sequence

Time limit: 0.5 second
Memory limit: 64 MB
There is a sequence of integer numbers A1, A2, …, AS, and a positive integer N. It's known that all elements of the sequence {Ai} satisfy the restriction 0 ≤ Ai ≤ 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 {Ai} and a number N will answer the question: is it true that for all 1 ≤ i ≤ j ≤ S the following inequality holds:
Ai + Ai+1 + … + Aj ≤ (ji + 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 {Ai}.

Output

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

Samples

inputoutput
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