#include <cstdio>
#include <algorithm>
#include <map>
using namespace std;
int main() {
	int N;
	long long K, ans = 0;
	scanf("%d %lld", &N, &K);
	long long A[N + 1];
	A[0] = 0;
	for (int i = 1; i <= N; ++i) scanf("%lld", &A[i]);
	map<long long, long long> hi;
	int lower = 0;
	for (int i = 1; i <= N; ++i) A[i] += A[i - 1] - 1;
	for (int i = 1; i <= N; ++i) A[i] %= K;
	hi[A[0]] = 1;
	for (int i = 1; i <= N; ++i) {
		if (i - lower >= K) --hi[A[lower++]];
		ans += hi[A[i]];
		++hi[A[i]];
	}
	printf("%lld", ans);
	return 0;
}
### Prompt

Develop a solution in Cpp to the problem described below:

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

### Response

```cpp
#include <cstdio>
#include <algorithm>
#include <map>
using namespace std;
int main() {
	int N;
	long long K, ans = 0;
	scanf("%d %lld", &N, &K);
	long long A[N + 1];
	A[0] = 0;
	for (int i = 1; i <= N; ++i) scanf("%lld", &A[i]);
	map<long long, long long> hi;
	int lower = 0;
	for (int i = 1; i <= N; ++i) A[i] += A[i - 1] - 1;
	for (int i = 1; i <= N; ++i) A[i] %= K;
	hi[A[0]] = 1;
	for (int i = 1; i <= N; ++i) {
		if (i - lower >= K) --hi[A[lower++]];
		ans += hi[A[i]];
		++hi[A[i]];
	}
	printf("%lld", ans);
	return 0;
}
```