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;
const int N = 2e5+5;
typedef long long i64;
int n, k, p[N], t[N], ans, cnt; i64 s;
void add(int x, int d) { for( ; x <= n; x += x&-x) t[x] += d; }
int ask(int x) { int y = 0; for( ; x; x ^= x&-x) y += t[x]; return y; }
int main()
{
    scanf("%d%d", &n, &k); for(int i = 1; i <= n; ++i) scanf("%d", p+i), ++p[i];
    for(int i = k; i; --i) s += ask(p[i]), add(p[i], 1); ans = s > 0, cnt = s == 0;
    for(int i = k+1, w = 0, v; i <= n; ++i) 
    {
        w = (v = ask(p[i-k]-1)) > 0, add(p[i-k], -1), s -= v,
        w |= (v = k-1-ask(p[i])) > 0, add(p[i], 1), s += v, 
        ans += w&&s > 0, cnt += s == 0;
    }
    printf("%d\n", ans+(cnt > 0));
    return 0;
}