Problem Statement

Given are a sequence of $N$ positive integers $A_1, A_2, \ldots, A_N$, and a positive integer $K$.

Find the number of non-empty contiguous subsequences in $A$ such that the remainder when dividing the sum of its elements by $K$ is equal to the number of its elements. We consider two subsequences different if they are taken from different positions, even if they are equal sequences.

Constraints

• All values in input are integers.
• $1 \leq N \leq 2\times 10^5$
• $1 \leq K \leq 10^9$
• $1 \leq A_i \leq 10^9$

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \cdots A_N

Output

Print the number of subsequences that satisfy the condition.