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 mod 1000000007
#define mod998 998244353
#define sp ' '
#define intmax 2147483647
#define llmax 9223372036854775807
#define mkp make_pair
typedef long long ll;
using namespace std;

int N, K, P[200000], c, a[200000];
set<int>st;
bool f;
int main() {
	cin >> N >> K;
	for (int i = 0; i < N; ++i) {
		cin >> P[i];
	}
	for (int i = 1; i < N; ++i) {
		if (P[i - 1] < P[i]) {
			a[i] = a[i - 1] + 1;
		}
	}
	for (int i = 0; i < K; ++i) {
		st.insert(P[i]);
	}
	c = 1;
	if (a[K - 1] >= K - 1) {
		f = true;
	}
	for (int i = K; i < N; ++i) {
		auto it = st.end();
		--it;
		auto it2 = st.begin();
		if (!(*it < P[i] && *it2 == P[i - K])) {
			++c;
			if (a[i] >= K - 1) {
				if (!f)f = true;
				else --c;
			}
		}
		st.erase(P[i - K]);
		st.insert(P[i]);
	}
	cout << c << endl;
}