You are given an array with \(N\) integers ranging from \(-10^9\) to \(10^9\). Check whether or not all subarray sums are less than or equal to \(K\).

A subarray is a non-empty contiguous segment of an array. For example, \([1, 3, -2]\) is a subarray of \([0, 1, 1, 3, -2, 4 5]\).

Input Specification

The first line of the input will contain two integers \(N\) \((1 \le N \le 2 \cdot 10^5)\) and \(K\) \((-10^{14} \le K \le 10^{14})\).

The second line of the input will contain \(N\) integers ranging from \(-10^9\) to \(10^9\) inclusive, each separated by a space.

Note that C++ and Java users will need to use long long or long datatypes to store \(K\).

Output Specification

Output YES if all subarray sums are less than or equal to \(K\), and NO otherwise.

Subtasks

Subtask 1 [30%]

\(1 \le N \le 300\)

Subtask 2 [30%]

\(1 \le N \le 2000\)

Subtask 3 [40%]

No additional constraints.

Sample Input

7 8
5 -1 -1 2 3 1 -2

Sample Output

NO

Sample Explanation

The sum of the subarray \([5, -1, -1, 2, 3, 1]\) exceeds the value \(8\).