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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dx = { 0, 1, 0, -1 };
        static readonly int[] dy = { 1, 0, -1, 0 };
        static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>>G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();

        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            var input = cin.ReadSplit();
            int N = input[0];
            int K = input[1];
            var P = cin.ReadSplit();

            var l = new List<int>();
            int len = 0;int prev = -1;
            for(var i = 0; i < N; i++)
            {
                if (P[i] < prev) { l.Add(len);len = 0; }
                len++;
                prev = P[i];
                if (i == N - 1) { l.Add(len); }
            }
            //Console.WriteLine(string.Join(",", l));
            long ans = N - K + 1;
            foreach(var x in l)
            {
                ans -= Max(0, x - K + 1);
            }
            if (ans < N - K + 1) { ans++; }
            var sgmin = new SegmentTree<int>(N, Min, INF);
            var sgmax = new SegmentTree<int>(N, Max, -1);
            for(var i = 0; i < N; i++)
            {
                sgmin.Assign(i, P[i]);
                sgmax.Assign(i, P[i]);
            }
            sgmax.Set_All();
            sgmin.Set_All();

            
            for(var i = 0; i + K < N; i++)
            {
                //Console.WriteLine($"{i}:{P[i]} < {sgmin.Query_Answer(i + 1, i + K)} < {sgmax.Query_Answer(i + 1, i + K)} < {P[i + K]}");
                if (P[i] < sgmin.Query_Answer(i + 1, i + K) && P[i + K] > sgmax.Query_Answer(i + 1, i + K))
                {
                    ans--;
                }
            }
            Console.WriteLine(ans);

            //Console.Out.Flush();
        }
        //5 3
        //0 2 1 4 3
        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }

        }
    }
    public class SegmentTree<T>
    {
        int n;
        T[] Tree;
        Func<T, T, T> f;
        T ex;
        public SegmentTree(int size, Func<T, T, T> fun, T exvalue)
        {
            f = fun;
            ex = exvalue;
            n = 1;
            while (n < size) n <<= 1;
            Tree = new T[(n << 1) - 1];
            for (var i = 0; i < Tree.Length; i++) Tree[i] = ex;
        }
        public SegmentTree(int size, Func<T, T, T> f, T exvalue, T initial) : this(size, f, exvalue)
        {
            for (var i = 0; i < size; i++) Tree[i + n - 1] = initial;
            Set_All();
        }

        public void Set_All()
        {
            for (var i = n - 2; i >= 0; i--)
            {
                Tree[i] = f(Tree[(i << 1) + 1], Tree[(i << 1) + 2]);
            }
        }

        public void Assign(int ind, T val)
        {
            Tree[ind + n - 1] = val;
        }
        public void Update(int ind)
        {
            int i = ind + n - 1;
            while (i > 0)
            {
                i = (i - 1) >> 1;
                Tree[i] = f(Tree[(i << 1) + 1], Tree[(i << 1) + 2]);
            }
        }

        public void Query_Update(int ind, T val)
        {
            Assign(ind, val);
            Update(ind);
        }
        public T Query_Answer(int l, int r) //[l,r)
        {
            return Scanning(l, r, 0, 0, n);
        }
        private T Scanning(int l, int r, int ind, int ind_l, int ind_r)
        {
            if (ind_r <= l || r <= ind_l) { return ex; }
            if (l <= ind_l && ind_r <= r) { return Tree[ind]; }
            return f(Scanning(l, r, (ind << 1) + 1, ind_l, (ind_l + ind_r) >> 1), Scanning(l, r, (ind << 1) + 2, (ind_l + ind_r) >> 1, ind_r));
        }

        public T Look(int ind)
        {
            return Tree[ind + n - 1];
        }
        public void Debug_Display_All()
        {
            for (var i = 0; i < n; i++) Console.Write($"{Tree[i + n - 1]} ");
            Console.WriteLine();
        }
    }
    public class Scanner
    {
        public int[] ReadSplit()
        {
            return ConvertAll(Console.ReadLine().Split(), int.Parse);
        }
        public long[] ReadSplitL()
        {
            return ConvertAll(Console.ReadLine().Split(), long.Parse);
        }
        public double[] ReadSplitD()
        {
            return ConvertAll(Console.ReadLine().Split(), double.Parse);
        }
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
        static public void Swap<T>(ref T a, ref T b)
        {
            T keep = a;
            a = b;
            b = keep;
        }

        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for (var i = 0; i < n; i++)
            {
                for (var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }

        static long LPow(int a, int b)
        {
            return (long)Pow(a, b);
        }
    }
}