Maximum Contiguous Tree Height Sum

You are given n trees with non-negative integer heights and a maximum allowed total height k. Your task is to find a contiguous segment of trees such that the sum of their heights is as large as possible without exceeding k. In other words, you need to maximize the sum

[ S = \sum_{i=l}^{r} h_i]

subject to the constraint that \(S \le k\). If no valid segment exists, the answer is 0.

Input Format

The first line contains two integers n and k separated by a space, where n is the number of trees and k is the maximum allowed total height.

The second line contains n space-separated integers representing the heights of the trees.

Output Format

Output a single integer representing the maximum possible total height of a contiguous segment of trees under the given constraint.

Note: If no contiguous segment satisfies the condition, output 0.

inputFormat

The input consists of two lines:

1. The first line contains two space-separated integers n and k. Here, n (1 ≤ n ≤ 10⁵) represents the number of trees and k (0 ≤ k ≤ 10⁹) is the maximum allowed total height.
2. The second line contains n space-separated integers, each representing the height of a tree. Each height is a non-negative integer.

outputFormat

Output a single integer which is the maximum total height of any contiguous segment of trees such that their sum does not exceed k.

## sample

5 10
3 1 4 2 5

10