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;
#define rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, x, n) for(int i = x; i < n; i++)
#define rep3(i, x, n) for(int i = x; i > n; i--)
const long long MOD = 1e9+7;
const long long INF = 1e15;
typedef long long ll;
typedef pair<ll, ll> P;

int main(){
    int N, K;
    cin >> N >> K;
    int P[N];
    rep(i, N) cin >> P[i];
    int count = 0;
    int pos = 0;
    while(pos < N){
        int j = 1;
        while(pos+j < N && P[pos+j-1] < P[pos+j]) j++;
        if(j >= K) count++;
        pos += j;
    }
    set<int> s;
    rep(i, K) s.insert(P[i]);
    int ans = 1;
    rep(i, N-K){
        s.insert(P[i+K]);
        set<int>::iterator ite1, ite2;;
        ite1 = s.find(P[i]);
        ite2 = s.find(P[i+K]);
        ite2++;
        if(ite1 != s.begin() || ite2 != s.end()) ans++;
        s.erase(P[i]);
    }
    if(count >= 2) ans -= count-1;
    cout << ans << endl;
}