In the courts of ancient Egypt, the god Anubis weighs the souls of the dead in a long ceremonial line. There are ~N~ souls waiting to be judged, and each soul has a known weight of virtue in grams. Anubis must choose exactly ~X~ grams for a rite of passage. Because the procession is sacred, he may only select a contiguous group of souls and will not rearrange their order.

Given the weights of the souls in order, find out how many ways Anubis can choose a contiguous group of souls whose total weight is exactly ~X~.

Input

The first line will contain two integers, ~N~ - the number of souls in the procession (~1 \leq N \leq 10^6~), and ~X~ - the target weight (~0 \leq X \leq 10^9~)

There will then be ~N~ integers, where ~W_i~ represents the weight of the ~i^{th}~ cow (~1 \leq W \leq 10^6~)

Output

Output the number of different ways Anubis can get exactly ~X~ grams from the souls.

Example

Input

5 300
100 200 150 50 100

Output

2

Explanation: Indices [0, 1] sum to 300 (100 + 200), and indices [2, 4] sum to 300 (150 + 50 + 100)