Cords

Jaś received $n$ cords from his grandfather and laid them out in a straight line, one next to another. Any two adjacent cords can be joined into a single cord whose length equals the sum of the two lengths. A cord formed this way can be joined again with an adjacent cord.

Jaś wants every cord he is left with to be at least as long as his own height $w$, while keeping as many cords as possible. Because only adjacent cords may be joined, each final cord is the concatenation of a contiguous block of the original cords.

Find the maximum number of cords Jaś can end up with. If joining all of the cords into one still gives a length shorter than $w$, then no valid arrangement exists, so output $0$.

The first line contains two integers $n$ and $w$ ($1 \le n, w \le 10^6$), the number of cords and Jaś's height.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$), the lengths of the cords from left to right.

Print a single integer: the maximum number of cords Jaś can obtain, where every cord has length at least $w$.