Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

5 4
1 4 2 3 5

Sample Output 1

4

Four sequences satisfy the condition: (1), (4,2), (1,4,2), and (5).

Sample Input 2

8 4
4 2 4 2 4 2 4 2

Sample Output 2

7

(4,2) is counted four times, and (2,4) is counted three times.

Sample Input 3

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

Sample Output 3

8

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.PrintWriter;
import java.util.Scanner;

public class Main {

    static Scanner sc = new Scanner(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
    	int N = nextInt();
    	int K = nextInt();
    	int[] A = new int[N];
    	int Answer = 0;

    	for (int i = 0; i < N; i++) {
    		int test = nextInt() % K;
    		if (test == 1) {
    			Answer++;
    		}
    		A[i] = test;
    	}

    	for (int i = 2; i <= N; i++) {
    		for (int j = 0; j <= (N - i); j++) {
    			double aaa = 0;
    			for (int k = 0; k < i; k++) {
    				aaa += A[j + k];
    			}
    			if (aaa % K == i) {
    				Answer++;
    			}
    		}
    	}
    	println(Answer);
    }

    static int nextInt() {
        return Integer.parseInt(next());
    }

    static String next() {
        return sc.next();
    }

    static String nextLine(){
        return sc.nextLine();
    }

    static void println(Object o) {
        out.println(o);
        out.flush();
    }
}