p02851 AtCoder Beginner Contest 146 - Rem of Sum is Num
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.

Examples

Input

5 4
1 4 2 3 5


Output

4


Input

8 4
4 2 4 2 4 2 4 2


Output

7


Input

10 7
14 15 92 65 35 89 79 32 38 46


Output

8
```python
from collections import defaultdict

def gets():
  return list(map(int, input().split()))

N, K = gets()
A = gets()

S = [0] * (N + 1)
for i in range(N):
  S[i + 1] = (S[i] + A[i] - 1) % K

cnt = defaultdict(int)
ans = 0
cnt[0] += 1
for i in range(1, N+1):
  if i - K >= 0:
    cnt[S[i - K]] -= 1
  ans += cnt[S[i]]
  cnt[S[i]] += 1

print(ans)

```