#include <bits/stdc++.h>
using namespace std;
#define MAXNUM 211111
#define rep(i,s,t) for(int i=s;i<t;i++)
typedef long long ll;
ll sum[MAXNUM];
unordered_map<ll,int> mm;
int main()
{
    int n,k;scanf("%d%d",&n,&k);
    mm[0]++;ll res=0;
    rep(i,1,n+1){
        scanf("%lld",&sum[i]),sum[i]+=sum[i-1],mm[(sum[i]-i+k)%k]++;
        if(i-k>=0)mm[(sum[i-k]-(i-k)+k)%k]--;
        res+=mm[(sum[i]-i+k)%k]-1;
    }
    printf("%lld\n",res);
}
### Prompt

Construct a CPP code solution to the problem outlined:

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;
#define MAXNUM 211111
#define rep(i,s,t) for(int i=s;i<t;i++)
typedef long long ll;
ll sum[MAXNUM];
unordered_map<ll,int> mm;
int main()
{
    int n,k;scanf("%d%d",&n,&k);
    mm[0]++;ll res=0;
    rep(i,1,n+1){
        scanf("%lld",&sum[i]),sum[i]+=sum[i-1],mm[(sum[i]-i+k)%k]++;
        if(i-k>=0)mm[(sum[i-k]-(i-k)+k)%k]--;
        res+=mm[(sum[i]-i+k)%k]-1;
    }
    printf("%lld\n",res);
}
```