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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define INF 2000000000
using namespace std;
typedef long long ll;
int read(){
    int f = 1, x = 0;
    char c = getchar();
    while(c < '0' || c > '9'){if(c == '-') f = -f; c = getchar();}
    while(c >= '0' && c <= '9')x = x * 10 + c - '0', c = getchar();
    return f * x; 
}
int n, k, a[200005];
set<int> s1, s2;
void init(){
    n = read(), k = read();
    for (int i = 0; i < n; ++i)
        a[i] = read();
}
void solve(){
    int ans = 1, cnt = 0;
    for (int i = 0; i < k; ++i)
        s1.insert(a[i]), s2.insert(-a[i]);
    for (int i = 1; i < k; ++i)
        if (a[i] > a[i - 1]) ++cnt;
    bool flag = false;
    for (int i = k; i < n; ++i){
        if (cnt == k - 1) flag = true;
        s2.insert(-a[i]), s2.erase(-a[i - k]);
        if (a[i - k + 1] > a[i - k]) --cnt;
        if (a[i] > a[i - 1]) ++cnt;
        if (a[i - k] != *s1.begin() || -a[i] != *s2.begin()){
            if (cnt != k - 1 || !flag) ++ans;
        }
        s1.insert(a[i]), s1.erase(a[i - k]);
    }
    printf("%d\n", ans);
}
int main(){
    init();
    solve();
    return 0;
}