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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <strings.h>

int
cmp(const void *a, const void *b)
{
    return *(int *)(a)-*(int *)(b);
}

int
main(int argc, char *argv[])
{
    int N, K;
    int P[200000];
    int Q[200000];
    int R[200000];
    int i, j;
    int num=0;

    scanf("%d%d", &N, &K);
    for (i=0; i<N; i++) {
        scanf("%d", P+i);
    }
    if (N==K) {
        printf("1\n");
        return 0;
    }
    bcopy(P, R, N);
    for (i=0; i<N-K; i++) {
        bcopy(P, Q, N);
        qsort(Q+i, K, sizeof(int), cmp);
        for (j=0; j<N; j++) {
            if (Q[j]!=R[j]) {
                bcopy(Q, R, N);
                continue;
            }
        }
        num++;
    }
    printf("%d\n", num);
    return 0;
}