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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using static Assistant.Input;
using static Assistant.Debug;
using System.Linq;
using Assistant;

namespace AGC038B
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = RInt;
            var K = RInt;
            var P2 = RInts;
            var P = new int[N + 1];
            for (int i = 0; i < N; i++)
            {
                P[i] = P2[i];
            }
            P[N] = int.MaxValue;

            // 単調増加？
            int[] rev = new int[N + 1];
            for (int i = 0; i < N; i++)
            {
                if (P[i] > P[i + 1]) rev[i] = 1;
            }
            for (int i = 0; i < N; i++)
            {
                rev[i + 1] += rev[i];
            }
            int revCount = 0;
            int last = -1;
            for (int i = 0; i < N - K; i++)
            {
                if (rev[i] != last && rev[i] == rev[i + K - 1]) { revCount++; last=rev[i]; }
            }

            Set<int> set = new Set<int>();
            for (int i = 0; i <= K; i++)
            {
                set.Add(P[i]);
            }

            int ans = 0;
            bool active = false;
            for (int i = 0; i < N - K + 1; i++)
            {
                if (set.Min == P[i] && P[i + K] == set.Max)
                {
                    if (!active)
                    {
                        ans++;
                        active = true;
                    }
                }
                else
                {
                    if (active) active = false;
                    else ans++;
                }

                set.Remove(P[i]);
                if (i < N - K) set.Add(P[i + K + 1]);
            }

            if (revCount > 1)
            {
                ans -= revCount - 1;
            }

            Console.WriteLine(ans);
            //Console.WriteLine(revCount);
            Draw1D(rev);
        }
    }

    public class Set<T>
    {
        Node root;
        readonly IComparer<T> comparer;
        readonly Node nil;
        public bool IsMultiSet { get; set; }
        public Set(IComparer<T> comparer)
        {
            nil = new Node(default(T));
            root = nil;
            this.comparer = comparer;
        }
        public Set(Comparison<T> comparison) : this(Comparer<T>.Create(comparison)) { }
        public Set() : this(Comparer<T>.Default) { }
        public Set(bool isMultiSet) : this(Comparer<T>.Default) { IsMultiSet = isMultiSet; }
        public bool Add(T v)
        {
            return insert(ref root, v);
        }
        public bool Remove(T v)
        {
            return remove(ref root, v);
        }
        public T this[int index] { get { return find(root, index); } }
        public T Min { get { return this[0]; } }
        public T Max { get { return this[Count - 1]; } }
        public int Count { get { return root.Count; } }
        public void RemoveAt(int k)
        {
            if (k < 0 || k >= root.Count) throw new ArgumentOutOfRangeException();
            removeAt(ref root, k);
        }
        public T[] Items
        {
            get
            {
                var ret = new T[root.Count];
                var k = 0;
                walk(root, ret, ref k);
                return ret;
            }
        }
        void walk(Node t, T[] a, ref int k)
        {
            if (t.Count == 0) return;
            walk(t.lst, a, ref k);
            a[k++] = t.Key;
            walk(t.rst, a, ref k);
        }

        bool insert(ref Node t, T key)
        {
            if (t.Count == 0) { t = new Node(key); t.lst = t.rst = nil; t.Update(); return true; }
            var cmp = comparer.Compare(t.Key, key);
            bool res;
            if (cmp > 0)
                res = insert(ref t.lst, key);
            else if (cmp == 0)
            {
                if (IsMultiSet) res = insert(ref t.lst, key);
                else return false;
            }
            else res = insert(ref t.rst, key);
            balance(ref t);
            return res;
        }
        bool remove(ref Node t, T key)
        {
            if (t.Count == 0) return false;
            var cmp = comparer.Compare(key, t.Key);
            bool ret;
            if (cmp < 0) ret = remove(ref t.lst, key);
            else if (cmp > 0) ret = remove(ref t.rst, key);
            else
            {
                ret = true;
                var k = t.lst.Count;
                if (k == 0) { t = t.rst; return true; }
                if (t.rst.Count == 0) { t = t.lst; return true; }


                t.Key = find(t.lst, k - 1);
                removeAt(ref t.lst, k - 1);
            }
            balance(ref t);
            return ret;
        }
        void removeAt(ref Node t, int k)
        {
            var cnt = t.lst.Count;
            if (cnt < k) removeAt(ref t.rst, k - cnt - 1);
            else if (cnt > k) removeAt(ref t.lst, k);
            else
            {
                if (cnt == 0) { t = t.rst; return; }
                if (t.rst.Count == 0) { t = t.lst; return; }

                t.Key = find(t.lst, k - 1);
                removeAt(ref t.lst, k - 1);
            }
            balance(ref t);
        }
        void balance(ref Node t)
        {
            var balance = t.lst.Height - t.rst.Height;
            if (balance == -2)
            {
                if (t.rst.lst.Height - t.rst.rst.Height > 0) { rotR(ref t.rst); }
                rotL(ref t);
            }
            else if (balance == 2)
            {
                if (t.lst.lst.Height - t.lst.rst.Height < 0) rotL(ref t.lst);
                rotR(ref t);
            }
            else t.Update();
        }

        T find(Node t, int k)
        {
            if (k < 0 || k > root.Count) throw new ArgumentOutOfRangeException();
            for (; ; )
            {
                if (k == t.lst.Count) return t.Key;
                else if (k < t.lst.Count) t = t.lst;
                else { k -= t.lst.Count + 1; t = t.rst; }
            }
        }
        public int LowerBound(T v)
        {
            var k = 0;
            var t = root;
            for (; ; )
            {
                if (t.Count == 0) return k;
                if (comparer.Compare(v, t.Key) <= 0) t = t.lst;
                else { k += t.lst.Count + 1; t = t.rst; }
            }
        }
        public int UpperBound(T v)
        {
            var k = 0;
            var t = root;
            for (; ; )
            {
                if (t.Count == 0) return k;
                if (comparer.Compare(t.Key, v) <= 0) { k += t.lst.Count + 1; t = t.rst; }
                else t = t.lst;
            }
        }

        void rotR(ref Node t)
        {
            var l = t.lst;
            t.lst = l.rst;
            l.rst = t;
            t.Update();
            l.Update();
            t = l;
        }
        void rotL(ref Node t)
        {
            var r = t.rst;
            t.rst = r.lst;
            r.lst = t;
            t.Update();
            r.Update();
            t = r;
        }


        class Node
        {
            public Node(T key)
            {
                Key = key;
            }
            public int Count { get; private set; }
            public sbyte Height { get; private set; }
            public T Key { get; set; }
            public Node lst, rst;
            public void Update()
            {
                Count = 1 + lst.Count + rst.Count;
                Height = (sbyte)(1 + Math.Max(lst.Height, rst.Height));
            }
            public override string ToString()
            {
                return string.Format("Count = {0}, Key = {1}", Count, Key);
            }
        }
    }

}

namespace Assistant
{
    static class Input
    {
        static List<string> line = new List<string>();
        static int index = 0;
        static String RNext()
        {
            if (line.Count <= index) line.AddRange(Console.ReadLine().Split());
            return line[index++];
        }
        public static int RInt => int.Parse(RNext());
        public static long RLong => long.Parse(RNext());
        public static int[] RInts => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] RLongs => Console.ReadLine().Split().Select(long.Parse).ToArray();
        public static string RString => RNext();
        //以下未テスト
        public static int[] RIntsC(int c) => Enumerable.Repeat(0, c).Select(x => int.Parse(RNext())).ToArray();
        public static long[] RLongsC(int c) => Enumerable.Repeat(0, c).Select(x => long.Parse(RNext())).ToArray();
        public static char[][] RMap(int h) => Enumerable.Repeat(0, h).Select(x => Console.ReadLine().ToCharArray()).ToArray();
    }

    public struct Mlong
    {
        long _v;
        const long mod = 1000000007;
        public Mlong(long n = 0) : this() { _v = n >= mod ? n % mod : n; }

        public static implicit operator Mlong(long _x) => new Mlong(_x);
        public static implicit operator long(Mlong _x) => _x._v;
        public static Mlong operator +(Mlong m1, Mlong m2) { long m = m1._v + m2._v; return m >= mod ? m - mod : m; }
        public static Mlong operator -(Mlong m1, Mlong m2) { long m = m1._v - m2._v; return m >= 0 ? m : m + mod; }
        public static Mlong operator *(Mlong m1, Mlong m2) => m1._v * m2._v % mod;
        public static Mlong operator /(Mlong m1, Mlong m2) => m1._v * ModPow(m2._v, mod - 2) % mod;

        public static long ModPow(long a, long n)
        {
            if (n == 0) return 1;
            else if (n % 2 == 1) return a * ModPow(a, n - 1) % mod;
            else return ModPow(a * a % mod, n / 2);
        }

        static Mlong[] fac, finv, inv;
        public static void nCkInit(int max)
        {
            fac = new Mlong[max]; finv = new Mlong[max]; inv = new Mlong[max];
            fac[0] = fac[1] = 1;
            finv[0] = finv[1] = 1;
            inv[1] = 1;
            for (int i = 2; i < max; i++)
            {
                fac[i] = fac[i - 1] * i;
                inv[i] = mod - inv[mod % i] * (mod / i);
                finv[i] = finv[i - 1] * inv[i];
            }
        }

        public static Mlong nCk(int n, int k)
        {
            if (n < k) return 0;
            if (n < 0 || k < 0) return 0;
            return fac[n] * finv[k] * finv[n - k];
        }
    }

    static class Debug
    {
        static public void Draw2D<T>(T[,] map, int mode = 1)
        {
#if DEBUG
            int W = map.GetLength(0);
            int H = map.GetLength(1);

            string[,] map2 = new string[W + 1, H + 1];
            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (i == 0 && j == 0) map2[i, j] = 0.ToString();
                    else if (i == 0) map2[i, j] = (j - 1).ToString();
                    else if (j == 0) map2[i, j] = (i - 1).ToString();
                    else map2[i, j] = map[i - 1, j - 1].ToString();
                }
            }

            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (mode == 0) Console.Write(map2[i, j].Last());
                    if (mode == 1) Console.Write(map2[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
#endif
        }

        public static void Draw1D<T>(T[] array, int mode = 0)
        {
#if DEBUG
            Console.WriteLine(string.Join(" ", array));
#endif
        }
    }
}