#include<bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 2e5+10;
const int MOD = 1e9+7;

int a[N],n,m;

int main(){
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	
	cin >> n >> m;
	for(int i=1;i<=n;++i){
		cin >> a[i];
		a[i] = (a[i]+a[i-1]) % m;
	}

	ll ans = 0;
	map<int, int> mp;
	mp[0] = 1;
	for(int i=1;i<=n;++i){
		if(i>=m) --mp[(a[i-m]+m-i%m)%m];
		int x = (a[i]+m-i%m) % m;
		auto itr = mp.find(x);
		if(itr != mp.end()) ans += itr->second;
		++mp[x];
	}
	cout << ans << endl;
	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<bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 2e5+10;
const int MOD = 1e9+7;

int a[N],n,m;

int main(){
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	
	cin >> n >> m;
	for(int i=1;i<=n;++i){
		cin >> a[i];
		a[i] = (a[i]+a[i-1]) % m;
	}

	ll ans = 0;
	map<int, int> mp;
	mp[0] = 1;
	for(int i=1;i<=n;++i){
		if(i>=m) --mp[(a[i-m]+m-i%m)%m];
		int x = (a[i]+m-i%m) % m;
		auto itr = mp.find(x);
		if(itr != mp.end()) ans += itr->second;
		++mp[x];
	}
	cout << ans << endl;
	return 0;
}
```