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 $8$.