Problem: 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.

Examples

Input

5 3
0 2 1 4 3


Output

2


Input

4 4
0 1 2 3


Output

1


Input

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


Output

6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

#ifdef DEBUG
#include "inc/debug.hpp"
#else
#define debug(...) 42
#endif

bool sorted[200010];

int main() {
    int N, K;
    cin >> N >> K;
    vector<int> P(N);
    for (int i=0; i<N; ++i) cin >> P[i];

    int res = 0;
    
    int cnt = 0;
    for (int i=0; i<N; ++i) {
        if (i == 0 || P[i-1] < P[i]) cnt ++;
        else cnt = 1;
        if (K <= cnt) {
            sorted[i-K+1] = true;
            res = 1;
        };
    }

    set<int> st;
    for (int i=0; i<K; ++i) {
        st.insert(P[i]);
    }

    if ( ! sorted[0]) res ++;
    for (int i=1; i+K-1<N; ++i) {
        if (i > 1) st.erase(P[i-2]);
        st.insert(P[i+K-1]);

        if (sorted[i]) continue;
        if (P[i-1] == *st.begin() && P[i+K-1] == *st.rbegin()) continue;
        res ++;
    }
    cout << res << endl;

    return 0;
}