p02851 AtCoder Beginner Contest 146 - Rem of Sum is Num_16992
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
import java.util.*;

class Main {
	static final Integer ZERO = Integer.valueOf(0);
	Scanner sc;
	int N, K;
	HashMap<Integer, Integer> h;
	int[] S;
	
	private void calc() {
		sc = new Scanner(System.in);
		N = sc.nextInt();
		K = sc.nextInt();
		S = new int[N+1];
		h = new HashMap<>(N*4/3);
		
		S[0] = 0;
		for (int i = 1; i < N+1; i++)
			S[i] = (int)(((long)S[i-1] + (sc.nextInt() - 1))%K);
		long cnt = 0;
		for (int i = 1; i < N+1; i++) {
			h.put( S[i-1], h.getOrDefault(S[i-1], ZERO) + 1);
			if (i >= K) {
				int v = h.get(S[i-K]);
				if (v > 1) h.put(S[i-K], v-1);
				else h.remove(S[i-K]);
			}
			cnt += h.getOrDefault(S[i], ZERO);
		}
		System.out.println(cnt);
	}
	
	public static void main(String[] args) {
		new Main().calc();
	}
}
