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>
#define Rep(i, x, y) for (int i = x; i <= y; i ++)
#define Dwn(i, x, y) for (int i = x; i >= y; i --)
#define RepE(i, x) for (int i = pos[x]; i; i = g[i].nex)
#define ev g[i].y
#define eps 1e-10
#define fr first
#define sd second
using namespace std;
typedef long long ll;
typedef double db;
const int N = 200005, mod = 1000000007;
int n, m, T, q = 1, ans, a[N], k;
set<int> s;
int main()
{
	scanf ("%d%d", &n, &m);
	Rep(i, 1, n) {
		scanf ("%d", &a[i]);
	}
	a[0] = -1;
	Rep(i, 1, m) {
		s.insert(a[i]);
		if (i > 1) k += (a[i] < a[i - 1]);
	}
	if (k) ans ++;
	else ans += q, q = 0;
	Rep(i, m + 1, n) {
		k += (a[i] < a[i - 1]) - (a[i - m + 1] < a[i - m]);
		// cout << ans<<" "<<*s.begin()<<" "<<*(-- s.end())<<" "<<k<< endl;
		if (*s.begin() != a[i - m] || *(-- s.end()) > a[i]) {
			if (k) ans ++;
			else ans += q, q = 0;
		}
		s.erase(a[i - m]);
		s.insert(a[i]);
	}
	printf("%d\n", ans);
	return 0;
}