Longest Window Under Budget

Statement

You are given n positive integers and a budget S. Find the maximum length of a contiguous subarray whose sum is at most S. Print 0 if no single element fits.

Input

The first line has n and S. The second line has n positive integers.

Output

Print one integer: the maximum length.

Constraints

1 <= n <= 200000
1 <= a_i <= 10^9
1 <= S <= 10^15

Example 1

6 10
2 3 1 4 1 2

4

2+3+1+4 = 10 has length 4. No window of length 5 has sum at most 10.