Simple Subarray Sum

Problem Description

You are given an integer array $A$ of length $N$ and an integer $K$.

How many subarrays of $A$ have a sum exactly equal to $K$?

Input Format

The first line contains two integers $N$ and $K$: the size of array $A$ and the given integer $K$.

The second line contains $N$ integers giving the elements $A_1, \dots, A_N$ of the array.

Output Format

Output one integer: the answer.

Sample Input 1

6 5
8 -3 5 7 0 -4

Sample Output 1

3

There are three subarrays ($(A_1, A_2)$, $(A_3)$, and $(A_2, \dots, A_6)$) whose sum equals $K$.

Sample Input 2

2 -1000000000000000
1000000000 -1000000000

Sample Output 2

0

Constraints

$1 \leq N \leq 2 \times 10^5$, $|A_i| \leq 10^9$, $|K| \leq 10^{15}$.