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<cstring>
#define  N  210000
using  namespace  std;
int  st[N][30],ss[N][30],lo2[N];
int  n,m,ans=1;
inline  int  mymin(int  x,int  y){return  x<y?x:y;}
inline  int  mymax(int  x,int  y){return  x>y?x:y;}
inline  int  rmq1(int  x,int  y)
{
	int  k=lo2[y-x+1];
	return  mymin(st[k][x],st[k][y-(1<<k)+1]);
}
inline  int  rmq2(int  x,int  y)
{
	int  k=lo2[y-x+1];
	return  mymax(st[k][x],st[k][y-(1<<k)+1]);
}
int  main()
{
	scanf("%d%d",&n,&m);
	for(int  i=1;i<=n;i++){scanf("%d",&st[i][0]);ss[i][0]=st[i][0];}
	for(int  i=2;i<=n;i++)lo2[i]=(lo2[i>>1])+1;
	for(int  i=1;i<=lo2[n];i++)
	{
		for(int  j=n-(1<<i)+1;j>=1;j--)st[i][j]=mymin(st[i-1][j],st[i-1][j+(1<<(i-1))]);
	}
	for(int  i=1;i<=lo2[n];i++)
	{
		for(int  j=n-(1<<i)+1;j>=1;j--)ss[i][j]=mymax(ss[i-1][j],ss[i-1][j+(1<<(i-1))]);
	}
	for(int  i=n-m;i>=1;i--)
	{
		if(st[i][0]>rmq1(i+1,i+m-1)  ||  st[i+m][0]<rmq2(i+1,i+m-1))ans++;
	}
	printf("%d\n",ans);
	return  0;
}