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 \leq C_i \leq 10^9~

~1 \leq M \leq 10^{18}~

Subtask 1 [10%]

~1 \leq N \leq 100~

Subtask 2 [20%]

~1 \leq N \leq 2\,000~

Subtask 3 [70%]

~1 \leq N \leq 200\,000~

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