#510614 (C#(csc)) No.1112 冥界の音楽

• 問題: No.1112 冥界の音楽
• ユーザー: terry_u16
• 提出日時: 2020-07-11 11:22:24
• 言語: C#(csc) (csc 3.9.0)
• 結果: AC
• 実行時間: 121 ms / 2,000 ms
• コード長: 34,547 bytes
• コンパイル時間: 4,023 ms
• コンパイル使用メモリ: 122,496 KB
• 実行使用メモリ: 19,072 KB
• 最終ジャッジ日時: 2024-10-12 20:22:01
• 合計ジャッジ時間: 4,423 ms
• ジャッジサーバーID （参考情報）: judge3 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	29 ms; 18,432 KB
testcase_01	AC	28 ms; 18,560 KB
testcase_02	AC	28 ms; 18,176 KB
testcase_03	AC	28 ms; 18,176 KB
testcase_04	AC	28 ms; 18,176 KB
testcase_05	AC	29 ms; 18,560 KB
testcase_06	AC	30 ms; 18,560 KB
testcase_07	AC	28 ms; 18,432 KB
testcase_08	AC	27 ms; 18,176 KB
testcase_09	AC	28 ms; 18,176 KB
testcase_10	AC	28 ms; 18,432 KB
testcase_11	AC	30 ms; 18,304 KB
testcase_12	AC	29 ms; 18,176 KB
testcase_13	AC	31 ms; 18,304 KB
testcase_14	AC	58 ms; 18,560 KB
testcase_15	AC	36 ms; 18,432 KB
testcase_16	AC	28 ms; 18,176 KB
testcase_17	AC	38 ms; 18,560 KB
testcase_18	AC	39 ms; 18,432 KB
testcase_19	AC	28 ms; 18,304 KB
testcase_20	AC	30 ms; 18,432 KB
testcase_21	AC	56 ms; 18,432 KB
testcase_22	AC	58 ms; 18,560 KB
testcase_23	AC	34 ms; 18,432 KB
testcase_24	AC	28 ms; 18,560 KB
testcase_25	AC	28 ms; 18,304 KB
testcase_26	AC	28 ms; 18,176 KB
testcase_27	AC	28 ms; 18,304 KB
testcase_28	AC	29 ms; 18,432 KB
testcase_29	AC	28 ms; 18,176 KB
testcase_30	AC	67 ms; 18,560 KB
testcase_31	AC	28 ms; 18,304 KB
testcase_32	AC	65 ms; 18,304 KB
testcase_33	AC	29 ms; 18,304 KB
testcase_34	AC	29 ms; 18,176 KB
testcase_35	AC	28 ms; 18,432 KB
testcase_36	AC	121 ms; 19,072 KB

コンパイルメッセージ

Microsoft (R) Visual C# Compiler version 3.9.0-6.21124.20 (db94f4cc)
Copyright (C) Microsoft Corporation. All rights reserved.

ソースコード

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using YukicoderContest256.Extensions;
using YukicoderContest256.Questions;

namespace YukicoderContest256.Questions
{
    public class QuestionF : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var (kinds, progressions, length) = inputStream.ReadValue<int, int, long>();
            var initialVector = new ModVector(kinds * kinds);    // (i, j)の数はv[ik + j]にあると定義
            var transMatrix = new ModMatrix(kinds * kinds);

            for (int second = 0; second < kinds; second++)
            {
                initialVector[0 * kinds + second] = 1;
            }

            for (int i = 0; i < progressions; i++)
            {
                var (p, q, r) = inputStream.ReadValue<int, int, int>();
                p--;
                q--;
                r--;
                transMatrix[q * kinds + r, p * kinds + q] = 1;
            }

            var powMatrix = transMatrix.Pow(length - 2);
            var counts = powMatrix * initialVector;
            var result = Modular.Zero;

            for (int previous = 0; previous < kinds; previous++)
            {
                result += counts[previous * kinds];
            }

            yield return result;
        }

        public readonly struct Modular : IEquatable<Modular>, IComparable<Modular>
        {
            private const int DefaultMod = 1000000007;
            public int Value { get; }
            public static int Mod { get; set; } = DefaultMod;

            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public Modular(long value)
            {
                if (unchecked((ulong)value) < unchecked((ulong)Mod))
                {
                    Value = (int)value;
                }
                else
                {
                    Value = (int)(value % Mod);
                    if (Value < 0)
                    {
                        Value += Mod;
                    }
                }
            }

            private Modular(int value) => Value = value;
            public static Modular Zero => new Modular(0);
            public static Modular One => new Modular(1);

            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public static Modular operator +(Modular a, Modular b)
            {
                var result = a.Value + b.Value;
                if (result >= Mod)
                {
                    result -= Mod;    // 剰余演算を避ける
                }
                return new Modular(result);
            }

            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public static Modular operator -(Modular a, Modular b)
            {
                var result = a.Value - b.Value;
                if (result < 0)
                {
                    result += Mod;    // 剰余演算を避ける
                }
                return new Modular(result);
            }

            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public static Modular operator *(Modular a, Modular b) => new Modular((long)a.Value * b.Value);

            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public static Modular operator /(Modular a, Modular b) => a * Pow(b.Value, Mod - 2);

            // 需要は不明だけど一応
            public static bool operator ==(Modular left, Modular right) => left.Equals(right);
            public static bool operator !=(Modular left, Modular right) => !(left == right);
            public static bool operator <(Modular left, Modular right) => left.CompareTo(right) < 0;
            public static bool operator <=(Modular left, Modular right) => left.CompareTo(right) <= 0;
            public static bool operator >(Modular left, Modular right) => left.CompareTo(right) > 0;
            public static bool operator >=(Modular left, Modular right) => left.CompareTo(right) >= 0;

            public static implicit operator Modular(long a) => new Modular(a);
            public static explicit operator int(Modular a) => a.Value;
            public static explicit operator long(Modular a) => a.Value;

            public static Modular Pow(int a, int n)
            {
                switch (n)
                {
                    case 0:
                        return Modular.One;
                    case 1:
                        return a;
                    case int m when m >= 0: // ジャンプテーブル化はできなくなる
                        var p = Pow(a, m >> 1);             // m / 2
                        return p * p * Pow(a, m & 0x01);    // m % 2
                    default:
                        throw new ArgumentOutOfRangeException(nameof(n), $"べき指数{nameof(n)}は0以上の整数でなければなりません。");
                }
            }

            private static List<int> _factorialCache;
            private static List<int> FactorialCache => _factorialCache ??= new List<int>() { 1 };
            private static int[] FactorialInverseCache { get; set; }
            const int defaultMaxFactorial = 1000000;

            public static Modular Factorial(int n)
            {
                if (n < 0)
                {
                    throw new ArgumentOutOfRangeException(nameof(n), $"{nameof(n)}は0以上の整数でなければなりません。");
                }

                for (int i = FactorialCache.Count; i <= n; i++)  // Countが1（0!までキャッシュ済み）のとき1!～n!まで計算
                {
                    FactorialCache.Add((int)((long)FactorialCache[i - 1] * i % Mod));
                }
                return new Modular(FactorialCache[n]);
            }

            public static Modular Permutation(int n, int r)
            {
                CheckNR(n, r);
                return Factorial(n) / Factorial(n - r);
            }

            public static Modular Combination(int n, int r)
            {
                CheckNR(n, r);
                r = Math.Min(r, n - r);
                try
                {
                    return new Modular(FactorialCache[n]) * new Modular(FactorialInverseCache[r]) * new Modular(FactorialInverseCache[n - r]);
                }
                catch (Exception ex) when (ex is NullReferenceException || ex is ArgumentOutOfRangeException)
                {
                    throw new InvalidOperationException($"{nameof(Combination)}を呼び出す前に{nameof(InitializeCombinationTable)}により前計算を行う必要があります。", ex);
                }
            }

            public static void InitializeCombinationTable(int max = defaultMaxFactorial)
            {
                Factorial(max);
                FactorialInverseCache = new int[max + 1];

                var fInv = (Modular.One / Factorial(max)).Value;
                FactorialInverseCache[max] = fInv;
                for (int i = max - 1; i >= 0; i--)
                {
                    fInv = (int)((long)fInv * (i + 1) % Mod);
                    FactorialInverseCache[i] = fInv;
                }
            }

            public static Modular CombinationWithRepetition(int n, int r) => Combination(n + r - 1, r);

            private static void CheckNR(int n, int r)
            {
                if (n < 0)
                {
                    throw new ArgumentOutOfRangeException(nameof(n), $"{nameof(n)}は0以上の整数でなければなりません。");
                }
                if (r < 0)
                {
                    throw new ArgumentOutOfRangeException(nameof(r), $"{nameof(r)}は0以上の整数でなければなりません。");
                }
                if (n < r)
                {
                    throw new ArgumentOutOfRangeException($"{nameof(n)},{nameof(r)}", $"{nameof(r)}は{nameof(n)}以下でなければなりません。");
                }
            }

            public override string ToString() => Value.ToString();
            public override bool Equals(object obj) => obj is Modular m ? Equals(m) : false;
            public bool Equals([System.Diagnostics.CodeAnalysis.AllowNull] Modular other) => Value == other.Value;
            public int CompareTo([System.Diagnostics.CodeAnalysis.AllowNull] Modular other) => Value.CompareTo(other.Value);
            public override int GetHashCode() => Value.GetHashCode();
        }

        public class ModMatrix
        {
            readonly Modular[] _values;
            public int Height { get; }
            public int Width { get; }

            public Span<Modular> this[int row]
            {
                [MethodImpl(MethodImplOptions.AggressiveInlining)]
                get => _values.AsSpan(row * Width, Width);
            }

            public Modular this[int row, int column]
            {
                [MethodImpl(MethodImplOptions.AggressiveInlining)]
                get
                {
                    if (unchecked((uint)row) >= Height)
                        ThrowsArgumentOutOfRangeException(nameof(row));
                    else if (unchecked((uint)column) >= Width)
                        ThrowsArgumentOutOfRangeException(nameof(column));
                    return _values[row * Width + column];
                }
                [MethodImpl(MethodImplOptions.AggressiveInlining)]
                set
                {
                    if (unchecked((uint)row) >= Height)
                        ThrowsArgumentOutOfRangeException(nameof(row));
                    else if (unchecked((uint)column) >= Width)
                        ThrowsArgumentOutOfRangeException(nameof(column));
                    _values[row * Width + column] = value;
                }
            }

            public ModMatrix(int n) : this(n, n) { }

            public ModMatrix(int height, int width)
            {
                Height = height;
                Width = width;
                _values = new Modular[height * width];
            }

            public ModMatrix(Modular[][] values)
            {
                Height = values.Length;
                Width = values[0].Length;
                _values = new Modular[Height * Width];
                for (int row = 0; row < Height; row++)
                {
                    var span = _values.AsSpan(row * Width, Width);
                    values[row].AsSpan().CopyTo(span);
                }
            }

            public ModMatrix(Modular[,] values)
            {
                Height = values.GetLength(0);
                Width = values.GetLength(1);
                _values = new Modular[values.Length];
                for (int row = 0; row < Height; row++)
                {
                    var span = _values.AsSpan(row * Width, Width);
                    for (int column = 0; column < span.Length; column++)
                    {
                        span[column] = values[row, column];
                    }
                }
            }

            public ModMatrix(ModMatrix matrix)
            {
                Height = matrix.Height;
                Width = matrix.Width;
                _values = new Modular[matrix._values.Length];
                matrix._values.AsSpan().CopyTo(_values);
            }

            public static ModMatrix GetIdentity(int dimension)
            {
                var result = new ModMatrix(dimension, dimension);
                for (int i = 0; i < dimension; i++)
                {
                    result._values[i * result.Width + i] = 1;
                }
                return result;
            }

            public static ModMatrix operator+(ModMatrix a, ModMatrix b)
            {
                CheckSameShape(a, b);

                var result = new ModMatrix(a.Height, a.Width);
                for (int i = 0; i < result._values.Length; i++)
                {
                    result._values[i] = a._values[i] + b._values[i];
                }
                return result;
            }

            public static ModMatrix operator-(ModMatrix a, ModMatrix b)
            {
                CheckSameShape(a, b);

                var result = new ModMatrix(a.Height, a.Width);
                for (int i = 0; i < result._values.Length; i++)
                {
                    result._values[i] = a._values[i] - b._values[i];
                }
                return result;
            }

            public static ModMatrix operator*(ModMatrix a, ModMatrix b)
            {
                if (a.Width != b.Height)
                    throw new ArgumentException($"{nameof(a)}の列数と{nameof(b)}の行数は等しくなければなりません。");

                var result = new ModMatrix(a.Height, b.Width);
                for (int i = 0; i < result.Height; i++)
                {
                    var aSpan = a._values.AsSpan(i * a.Width, a.Width);
                    var resultSpan = result._values.AsSpan(i * result.Width, result.Width);
                    for (int k = 0; k < aSpan.Length; k++)
                    {
                        var bSpan = b._values.AsSpan(k * b.Width, b.Width);
                        for (int j = 0; j < resultSpan.Length; j++)
                        {
                            resultSpan[j] += aSpan[k] * bSpan[j];
                        }
                    }
                }
                return result;
            }

            public static ModVector operator*(ModMatrix matrix, ModVector vector)
            {
                if (matrix.Width != vector.Length)
                    throw new ArgumentException($"{nameof(matrix)}の列数と{nameof(vector)}の行数は等しくなければなりません。");

                var result = new ModVector(vector.Length);
                for (int i = 0; i < result.Length; i++)
                {
                    var matrixSpan = matrix[i];
                    for (int k = 0; k < matrixSpan.Length; k++)
                    {
                        result[i] += matrixSpan[k] * vector[k];
                    }
                }
                return result;
            }

            public ModMatrix Pow(long pow)
            {
                if (Height != Width)
                    throw new ArgumentException("累乗を行う行列は正方行列である必要があります。");
                if (pow < 0)
                    throw new ArgumentException($"{nameof(pow)}は0以上の整数である必要があります。");

                var powMatrix = new ModMatrix(this);
                var result = GetIdentity(Height);
                while (pow > 0)
                {
                    if ((pow & 1) > 0)
                    {
                        result *= powMatrix;
                    }
                    powMatrix *= powMatrix;
                    pow >>= 1;
                }
                return result;
            }

            private static void CheckSameShape(ModMatrix a, ModMatrix b)
            {
                if (a.Height != b.Height)
                    throw new InvalidOperationException($"{nameof(a)}の行数と{nameof(b)}の行数は等しくなければなりません。");
                else if (a.Width != b.Width)
                    throw new InvalidOperationException($"{nameof(a)}の列数と{nameof(b)}の列数は等しくなければなりません。");
            }

            private void ThrowsArgumentOutOfRangeException(string paramName) => throw new ArgumentOutOfRangeException(paramName);
            public override string ToString() => $"({Height}x{Width})matrix";
        }

        public class ModVector
        {
            readonly Modular[] _values;
            public int Length => _values.Length;

            public ModVector(int length) => _values = new Modular[length];

            public ModVector(ReadOnlySpan<Modular> vector)
            {
                _values = new Modular[vector.Length];
                vector.CopyTo(_values);
            }

            public ModVector(ModVector vector) : this(vector._values) { }

            public Modular this[int index]
            {
                get => _values[index];
                set => _values[index] = value;
            }

            public static ModVector operator+(ModVector a, ModVector b)
            {
                if (a.Length != b.Length)
                    throw new ArgumentException($"{nameof(a)}と{nameof(b)}の次元は等しくなければなりません。");

                var result = new ModVector(a.Length);
                for (int i = 0; i < result.Length; i++)
                {
                    result[i] = a[i] + b[i];
                }
                return result;
            }

            public static ModVector operator-(ModVector a, ModVector b)
            {
                if (a.Length != b.Length)
                    throw new ArgumentException($"{nameof(a)}と{nameof(b)}の次元は等しくなければなりません。");

                var result = new ModVector(a.Length);
                for (int i = 0; i < result.Length; i++)
                {
                    result[i] = a[i] - b[i];
                }
                return result;
            }

            public static Modular operator*(ModVector a, ModVector b)
            {
                if (a.Length != b.Length)
                    throw new ArgumentException($"{nameof(a)}と{nameof(b)}の次元は等しくなければなりません。");

                var result = Modular.Zero;
                for (int i = 0; i < a.Length; i++)
                {
                    result += a[i] * b[i];
                }
                return result;
            }

            public override string ToString() => $"({Length})vector";
        }
    }
}

namespace YukicoderContest256
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionF();
            var answers = question.Solve(Console.In);

            var writer = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(writer);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
            Console.Out.Flush();
        }
    }
}

#region Base Class

namespace YukicoderContest256.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }
}

#endregion

#region Graphs

namespace YukicoderContest256.Graphs
{
    public interface INode
    {
        public int Index { get; }
    }

    public interface IEdge<TNode> where TNode : INode
    {
        TNode From { get; }
        TNode To { get; }
    }

    public interface IWeightedEdge<TNode> : IEdge<TNode> where TNode : INode
    {
        long Weight { get; }
    }

    public interface IGraph<TNode, TEdge> where TEdge : IEdge<TNode> where TNode : INode
    {
        IEnumerable<TEdge> this[TNode node] { get; }
        IEnumerable<TEdge> Edges { get; }
        IEnumerable<TNode> Nodes { get; }
        int NodeCount { get; }
    }

    public interface IWeightedGraph<TNode, TEdge> : IGraph<TNode, TEdge> where TEdge : IWeightedEdge<TNode> where TNode : INode { }

    [StructLayout(LayoutKind.Auto)]
    public readonly struct BasicNode : INode, IEquatable<BasicNode>
    {
        public int Index { get; }

        public BasicNode(int index)
        {
            Index = index;
        }

        public override string ToString() => Index.ToString();
        public override bool Equals(object obj) => obj is BasicNode node && Equals(node);
        public bool Equals(BasicNode other) => Index == other.Index;
        public override int GetHashCode() => HashCode.Combine(Index);
        public static bool operator ==(BasicNode left, BasicNode right) => left.Equals(right);
        public static bool operator !=(BasicNode left, BasicNode right) => !(left == right);
        public static implicit operator BasicNode(int value) => new BasicNode(value);
    }

    [StructLayout(LayoutKind.Auto)]
    public readonly struct BasicEdge : IEdge<BasicNode>
    {
        public BasicNode From { get; }
        public BasicNode To { get; }

        public BasicEdge(int from, int to)
        {
            From = from;
            To = to;
        }

        public override string ToString() => $"{From}-->{To}";
    }

    [StructLayout(LayoutKind.Auto)]
    public readonly struct WeightedEdge : IWeightedEdge<BasicNode>
    {
        public BasicNode From { get; }
        public BasicNode To { get; }
        public long Weight { get; }

        public WeightedEdge(int from, int to) : this(from, to, 1) { }

        public WeightedEdge(int from, int to, long weight)
        {
            From = from;
            To = to;
            Weight = weight;
        }

        public override string ToString() => $"{From}--[{Weight}]-->{To}";
    }

    [StructLayout(LayoutKind.Auto)]
    public readonly struct GridNode : INode, IEquatable<GridNode>
    {
        public int Row { get; }
        public int Column { get; }
        public int Index { get; }

        public GridNode(int row, int column, int width)
        {
            Row = row;
            Column = column;
            Index = row * width + column;
        }

        public override string ToString() => $"({Row}, {Column})";
        public override int GetHashCode() => HashCode.Combine(Row, Column, Index);
        public override bool Equals(object obj) => obj is GridNode node && Equals(node);
        public bool Equals(GridNode other) => Row == other.Row && Column == other.Column && Index == other.Index;
        public void Deconstruct(out int row, out int column) { row = Row; column = Column; }
        public static bool operator ==(GridNode left, GridNode right) => left.Equals(right);
        public static bool operator !=(GridNode left, GridNode right) => !(left == right);
    }

    [StructLayout(LayoutKind.Auto)]
    public readonly struct GridEdge : IEdge<GridNode>
    {
        public GridNode From { get; }
        public GridNode To { get; }

        public GridEdge(GridNode from, GridNode to)
        {
            From = from;
            To = to;
        }

        public override string ToString() => $"({From.Row}, {From.Column})-->({To.Row}, {To.Column})";
    }

    public class BasicGraph : IGraph<BasicNode, BasicEdge>
    {
        private readonly List<BasicEdge>[] _edges;
        public IEnumerable<BasicEdge> this[BasicNode node] => _edges[node.Index];
        public IEnumerable<BasicEdge> Edges => Nodes.SelectMany(node => this[node]);
        public IEnumerable<BasicNode> Nodes => Enumerable.Range(0, NodeCount).Select(i => new BasicNode(i));
        public int NodeCount { get; }

        public BasicGraph(int nodeCount) : this(nodeCount, Enumerable.Empty<BasicEdge>()) { }

        public BasicGraph(int nodeCount, IEnumerable<BasicEdge> edges)
        {
            _edges = Enumerable.Repeat(0, nodeCount).Select(_ => new List<BasicEdge>()).ToArray();
            NodeCount = nodeCount;
            foreach (var edge in edges)
            {
                AddEdge(edge);
            }
        }

        public BasicGraph(int nodeCount, IEnumerable<IEnumerable<int>> distances)
        {
            _edges = new List<BasicEdge>[nodeCount];

            int i = 0;
            foreach (var row in distances)
            {
                _edges[i] = new List<BasicEdge>(nodeCount);
                int j = 0;
                foreach (var distance in row)
                {
                    if (distance == 1)
                    {
                        _edges[i].Add(new BasicEdge(i, j++));
                    }
                }
                i++;
            }
        }

        public void AddEdge(BasicEdge edge) => _edges[edge.From.Index].Add(edge);
    }

    public class WeightedGraph : IGraph<BasicNode, WeightedEdge>
    {
        private readonly List<WeightedEdge>[] _edges;
        public IEnumerable<WeightedEdge> this[BasicNode node] => _edges[node.Index];
        public IEnumerable<WeightedEdge> Edges => Nodes.SelectMany(node => this[node]);
        public IEnumerable<BasicNode> Nodes => Enumerable.Range(0, NodeCount).Select(i => new BasicNode(i));
        public int NodeCount { get; }

        public WeightedGraph(int nodeCount) : this(nodeCount, Enumerable.Empty<WeightedEdge>()) { }

        public WeightedGraph(int nodeCount, IEnumerable<WeightedEdge> edges)
        {
            _edges = Enumerable.Repeat(0, nodeCount).Select(_ => new List<WeightedEdge>()).ToArray();
            NodeCount = nodeCount;
            foreach (var edge in edges)
            {
                AddEdge(edge);
            }
        }

        public WeightedGraph(int nodeCount, IEnumerable<IEnumerable<int>> distances)
        {
            _edges = new List<WeightedEdge>[nodeCount];

            int i = 0;
            foreach (var row in distances)
            {
                _edges[i] = new List<WeightedEdge>(nodeCount);
                int j = 0;
                foreach (var distance in row)
                {
                    _edges[i].Add(new WeightedEdge(i, j++, distance));
                }
                i++;
            }
        }

        public void AddEdge(WeightedEdge edge) => _edges[edge.From.Index].Add(edge);
    }
}

#endregion


#region Extensions

namespace YukicoderContest256.Extensions
{
    public static class SearchExtensions
    {
        class LowerBoundComparer<T> : IComparer<T> where T : IComparable<T>
        {
            public int Compare(T x, T y) => 0 <= x.CompareTo(y) ? 1 : -1;
        }

        class UpperBoundComparer<T> : IComparer<T> where T : IComparable<T>
        {
            public int Compare(T x, T y) => 0 < x.CompareTo(y) ? 1 : -1;
        }

        // https://trsing.hatenablog.com/entry/2019/08/27/211038
        public static int GetGreaterEqualIndex<T>(this ReadOnlySpan<T> span, T inclusiveMin) where T : IComparable<T> => ~span.BinarySearch(inclusiveMin, new UpperBoundComparer<T>());
        public static int GetGreaterThanIndex<T>(this ReadOnlySpan<T> span, T exclusiveMin) where T : IComparable<T> => ~span.BinarySearch(exclusiveMin, new LowerBoundComparer<T>());
        public static int GetLessEqualIndex<T>(this ReadOnlySpan<T> span, T inclusiveMax) where T : IComparable<T> => ~span.BinarySearch(inclusiveMax, new LowerBoundComparer<T>()) - 1;
        public static int GetLessThanIndex<T>(this ReadOnlySpan<T> span, T exclusiveMax) where T : IComparable<T> => ~span.BinarySearch(exclusiveMax, new UpperBoundComparer<T>()) - 1;
        public static int GetGreaterEqualIndex<T>(this Span<T> span, T inclusiveMin) where T : IComparable<T> => ((ReadOnlySpan<T>)span).GetGreaterEqualIndex(inclusiveMin);
        public static int GetGreaterThanIndex<T>(this Span<T> span, T exclusiveMin) where T : IComparable<T> => ((ReadOnlySpan<T>)span).GetGreaterThanIndex(exclusiveMin);
        public static int GetLessEqualIndex<T>(this Span<T> span, T inclusiveMax) where T : IComparable<T> => ((ReadOnlySpan<T>)span).GetLessEqualIndex(inclusiveMax);
        public static int GetLessThanIndex<T>(this Span<T> span, T exclusiveMax) where T : IComparable<T> => ((ReadOnlySpan<T>)span).GetLessThanIndex(exclusiveMax);

        public static int BoundaryBinarySearch(Predicate<int> predicate, int ok, int ng)
        {
            // めぐる式二分探索
            while (Math.Abs(ok - ng) > 1)
            {
                int mid = (ok + ng) / 2;
                if (predicate(mid))
                {
                    ok = mid;
                }
                else
                {
                    ng = mid;
                }
            }
            return ok;
        }

        public static long BoundaryBinarySearch(Predicate<long> predicate, long ok, long ng)
        {
            while (Math.Abs(ok - ng) > 1)
            {
                long mid = (ok + ng) / 2;
                if (predicate(mid))
                {
                    ok = mid;
                }
                else
                {
                    ng = mid;
                }
            }
            return ok;
        }

        public static double Bisection(Func<double, double> f, double a, double b, double eps = 1e-9)
        {
            if (f(a) * f(b) >= 0)
            {
                throw new ArgumentException("f(a)とf(b)は異符号である必要があります。");
            }

            const int maxLoop = 100;
            double mid = (a + b) / 2;

            for (int i = 0; i < maxLoop; i++)
            {
                if (f(a) * f(mid) < 0)
                {
                    b = mid;
                }
                else
                {
                    a = mid;
                }
                mid = (a + b) / 2;
                if (Math.Abs(b - a) < eps)
                {
                    break;
                }
            }
            return mid;
        }
    }

    public static class StringExtensions
    {
        public static string Join<T>(this IEnumerable<T> source) => string.Concat(source);
        public static string Join<T>(this IEnumerable<T> source, char separator) => string.Join(separator, source);
        public static string Join<T>(this IEnumerable<T> source, string separator) => string.Join(separator, source);
    }

    public static class TextReaderExtensions
    {
        public static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        public static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        public static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        public static string ReadString(this TextReader reader) => reader.ReadLine();

        public static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        public static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        public static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        public static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);

        // Supports primitive type only.
        public static T1 ReadValue<T1>(this TextReader reader) => (T1)Convert.ChangeType(reader.ReadLine(), typeof(T1));

        public static (T1, T2) ReadValue<T1, T2>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            return (v1, v2);
        }

        public static (T1, T2, T3) ReadValue<T1, T2, T3>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
            return (v1, v2, v3);
        }

        public static (T1, T2, T3, T4) ReadValue<T1, T2, T3, T4>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
            var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
            return (v1, v2, v3, v4);
        }

        public static (T1, T2, T3, T4, T5) ReadValue<T1, T2, T3, T4, T5>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
            var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
            var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
            return (v1, v2, v3, v4, v5);
        }

        public static (T1, T2, T3, T4, T5, T6) ReadValue<T1, T2, T3, T4, T5, T6>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
            var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
            var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
            var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6));
            return (v1, v2, v3, v4, v5, v6);
        }

        public static (T1, T2, T3, T4, T5, T6, T7) ReadValue<T1, T2, T3, T4, T5, T6, T7>(this TextReader reader, char separator = ' ')
        {
            var inputs = ReadStringArray(reader, separator);
            var v1 = (T1)Convert.ChangeType(inputs[0], typeof(T1));
            var v2 = (T2)Convert.ChangeType(inputs[1], typeof(T2));
            var v3 = (T3)Convert.ChangeType(inputs[2], typeof(T3));
            var v4 = (T4)Convert.ChangeType(inputs[3], typeof(T4));
            var v5 = (T5)Convert.ChangeType(inputs[4], typeof(T5));
            var v6 = (T6)Convert.ChangeType(inputs[5], typeof(T6));
            var v7 = (T7)Convert.ChangeType(inputs[6], typeof(T7));
            return (v1, v2, v3, v4, v5, v6, v7);
        }
    }
}

#endregion