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>
#include <string.h>

int main(){
	int N,K;
	scanf("%d %d\n",&N,&K);
	char *P;
	P = (char*)malloc(N*sizeof(char));
	char *buff;
	buff = (char*)malloc((2*N+1)*sizeof(char));
	scanf("%[^\n]",buff);
	int i = 0;
    int ans = 0;
	for(i=0;i<N;i++){
		P[i]=buff[2*i];
	}
    int num_of_trial = N-K+1;
    free(buff);
    buff = malloc(K*sizeof(char));
    char **seg_sorted;
    seg_sorted = malloc(num_of_trial*sizeof(char*));
    for(i=0;i<num_of_trial;i++){
        seg_sorted[i]=malloc(N*sizeof(char));
        strncpy(seg_sorted[i],P,i);
        strncpy(buff,P[i],K);

    }
    for(i=0;i<num_of_trial;i++){

    }

	return 0;
}