Problem:
Score : 700 points

Problem Statement

Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).

Now, he will perform the following operation exactly once:

Choose K consecutive elements in P and sort them in ascending order.

Find the number of permutations that can be produced as P after the operation.

Constraints

2 \leq N \leq 200000

2 \leq K \leq N

0 \leq P_i \leq N-1

P_0,P_1,\cdots,P_{N-1} are all different.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
P_0 P_1 \cdots P_{N-1}

Output

Print the number of permutations that can be produced as P after the operation.

Sample Input 1

5 3
0 2 1 4 3

Sample Output 1

2

Two permutations can be produced as P after the operation: (0,1,2,4,3) and (0,2,1,3,4).

Sample Input 2

4 4
0 1 2 3

Sample Output 2

1

Sample Input 3

10 4
2 0 1 3 7 5 4 6 8 9

Sample Output 3

6

Solution in C (GCC 5.4.1) (judge verdict: Runtime Error)

#include<stdio.h>
#include<stdlib.h>
#define SIZE20 200000

typedef long long int ll;
typedef unsigned char u8;

int main(void){
    int N = 0, K = 0;
    int P[20];
    int i = 0, j = 0;
    ll cnt = 0, n = 0;

    scanf("%d %d", &N, &K);

    for(i = 0; i < N; i++){
        scanf("%d", &P[i]);
    }

    cnt = N-K+1;

    for(i = 0; i < N-K+1; i++){
        for(j = 0; j < K-1; j++){
            if(P[i+j] > P[i+j+1]){
                break;
            }
        }
        if(j == K-1){
            n++;
        }
    }

    n--;

    for(i = 0; i < N-K; i++){
        for(j = 1; j < K; j++){
            if((P[i] > P[i+j]) || (P[i+K] < P[i+j])){
                break;
            }
        }
        if(j == K){
            n+=1;
        }
    }

    printf("%lld", cnt-n);
    return 0;
}