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;

typedef long long ll;
ll N, K;
const ll MAX_N = 200000;
ll P[MAX_N];
set<ll> S;
ll KAsc;
ll R = 1;

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

  ll asc_cont = 0;
  for (ll i = 0; i < N - 1; ++i) {
    if (P[i] < P[i + 1]) {
      ++asc_cont;
      if (asc_cont == K - 1) ++KAsc;
    } else {
      asc_cont = 0;
    }
  }

  for (ll i = 0; i < K - 1; ++i) {
    S.insert(P[i]);
  }
  for (ll i = 0; i < N - K; ++i) {
    S.erase(P[i]);
    S.insert(P[i + K - 1]);
    if (!(P[i] < *S.begin() && *S.rbegin() < P[i + K])) {
      ++R;
    }
  }
  cout << R - (KAsc == 0 ? 0 : KAsc - 1) << endl;
  return 0;
}