Subarray Average of a Sequence

A sequence $A_1, A_2, \cdots, A_N$ of length $N$ is given. Count the number of intervals whose elements all have an average of exactly $K$.

The first line gives the size of the sequence $N$ and the desired average $K$. ($1 \le N \le 200,000$, $-10^9 \le K \le 10^9$)

The second line gives the sequence $A_1, A_2, \cdots, A_N$. ($1 \le i \le N$, $-10^9 \le A_i \le 10^9$)

Every number in the input is an integer.

Print the number of intervals whose elements all have an average of $K$.