Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

5 3
0 2 1 4 3

Sample Output 1

2

Two permutations can be produced as P after the operation: (0,1,2,4,3) and (0,2,1,3,4).

Sample Input 2

4 4
0 1 2 3

Sample Output 2

1

Sample Input 3

10 4
2 0 1 3 7 5 4 6 8 9

Sample Output 3

6

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<cstdio>
#include<cstdlib>
#include<cassert>
#include<iostream>
#include<set>
using namespace std;

inline int read()
{
	int x=0; bool f=1; char c=getchar();
	for(;!isdigit(c);c=getchar()) if(c=='-') f=0;
	for(; isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+(c^'0');
	if(f) return x;
	return -x;
}

const int N = 2e5;
int a[N+3];
int uf[N+3];
set<int> s;
int n,m;

int findfa(int u) {return u==uf[u]?u:uf[u]=findfa(uf[u]);}
int unionfa(int u,int v) {int uu = findfa(u),vv = findfa(v); if(uu!=vv) uf[uu] = vv;}

int main()
{
	scanf("%d%d",&n,&m);
	for(int i=0; i<=n; i++) uf[i] = i;
	for(int i=1; i<=n; i++) scanf("%d",&a[i]); int cur = 0;
	for(int i=1; i<=m; i++) {s.insert(a[i]); if(i>1) {cur += (a[i-1]<a[i]);}}
	for(int i=m; i<=n; i++)
	{
		if(i<n)
		{
			if(((*s.begin())==a[i-m+1]) && ((*s.rbegin())<a[i+1]))
			{
				unionfa(i-m+2,i-m+1);
			}
		}
		cur -= (a[i-m]<a[i-m+1]);
		if(cur==m-1) {unionfa(i-m+1,0);}
		cur += (a[i]<a[i+1]);
		s.erase(a[i-m+1]);
		s.insert(a[i+1]);
	}
	int cnt = 0,ans = 0;
	for(int i=0; i<=n-m+1; i++) {if(uf[i]==i) ans++; if(i&&findfa(i)==findfa(0)) cnt++;}
	if(cnt) printf("%d\n",ans);
	else printf("%d\n",ans-1);
	return 0;
}