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.

-----Sample Input-----
5 4
1 4 2 3 5

-----Sample Output-----
4

Four sequences satisfy the condition: (1), (4,2), (1,4,2), and (5).

见题面

见题面