Description

Given a sequence of positive integers $a_i$ of length $n$, divide it into consecutive segments such that the sum of each segment does not exceed $m$ (can be equal to $m$). Find the minimum number of segments needed to satisfy this requirement.

Input Format

The first line contains two positive integers $n$ and $m$, representing the length of the sequence and the maximum sum allowed for each segment.
The second line contains $n$ non-negative integers $a_i$ separated by spaces.
Constraints: $1≤n≤10^5$, $1≤a_i≤m≤10^4$.

Output Format

Output a single positive integer representing the minimum number of segments needed.

Sample

5 6
4 2 4 5 1

3