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 <iostream>
#include <set>
#include <vector>
#define rep(i, n) for (int i = 0; i < (n); ++i)
using namespace std;

int main(void) {
  ios::sync_with_stdio(false);
  int N, K;
  cin >> N >> K;
  vector<int> P(N);
  rep(i, N) cin >> P[i];

  int ascend = 1;
  set<int> hist;
  hist.emplace(P[0]);
  for (int i = 1; i < K; ++i) {
    hist.emplace(P[i]);
    ascend = (P[i - 1] < P[i]) ? ascend + 1 : 1;
  }

  int answer = 1;
  bool unsort0 = (ascend == K);
  bool unsort1 = false;
  for (int i = K; i < N; ++i) {
    bool not_change = ((P[i - K] == *hist.begin()) && (*hist.rbegin() < P[i]));
    hist.erase(P[i - K]);
    hist.emplace(P[i]);

    ascend = (P[i - 1] < P[i]) ? ascend + 1 : 1;
    if (K <= ascend)
      unsort1 = true;
    else if (!not_change)
      answer++;
  }

  if (!unsort0 && unsort1) answer++;
  cout << answer << endl;
  return 0;
}