For her birthday, Mimi received a set of $N$ pencil crayons. Mimi loves her beautiful pencil crayons. In fact, she loves them so much that she assigned each of them individual names, a backstory, and also a cuteness number, $C_i$.

One day, Mimi lent out her pencil crayons for an art class assignment. When the class ended, her friend returned the pencil crayons in a neat row. Mimi then asked her a curious question:

What is the longest contiguous subsequence where the sum of the cuteness numbers is strictly less than $M$?

Can you answer her question?

Constraints

For all subtasks:

$1\le C_i\le {10}^9$

$1\le M\le {10}^{18}$

Subtask 1 [10%]

$1\le N\le 100$

Subtask 2 [20%]

$1\le N\le 2000$

Subtask 3 [70%]

$1\le N\le 200000$

Input Specification

The first line of input will contain two space-separated integers, $N$ and $M$.
The second line of input will contain $N$ space-separated integers, $C_1,C_2,\dots ,C_N$.

Output Specification

A single integer, the length of the longest subarray where the sum of the cuteness numbers is strictly less than $M$.

Sample Input

5 3
1 1 1 2 3

Sample Output

2