Description

Given a positive integer sequence $A_i$ of length $N$, it needs to be divided into contiguous segments such that the sum of each segment does not exceed $M$ (it can be equal to $M$). The task is to find the minimum number of segments required to meet this condition.

Input Format

The first line contains two positive integers $N$ and $M$, representing the length of the sequence $A_i$ and the maximum allowed sum for each segment.

The second line contains $N$ space-separated non-negative integers $A_i$.

Output Format

The output file should contain a single positive integer, which is the minimum number of segments required.

Sample 1

5 6
4 2 4 5 1

3

Data Range and Hints

For $20\%$ of the data, $N\le 10$;

For $40\%$ of the data, $N\le 1000$;

For $100\%$ of the data, $N\le 10^5$, $M\le 10^9$, and $M$ is greater than the maximum value in the sequence.