結果
問題 |
No.3226 2×2行列累乗
|
ユーザー |
![]() |
提出日時 | 2025-08-08 21:45:45 |
言語 | C# (.NET 8.0.404) |
結果 |
AC
|
実行時間 | 65 ms / 2,000 ms |
コード長 | 49,982 bytes |
コンパイル時間 | 8,957 ms |
コンパイル使用メモリ | 169,828 KB |
実行使用メモリ | 199,340 KB |
最終ジャッジ日時 | 2025-08-08 21:45:57 |
合計ジャッジ時間 | 11,787 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 27 |
コンパイルメッセージ
復元対象のプロジェクトを決定しています... /home/judge/data/code/main.csproj を復元しました (111 ミリ秒)。 main -> /home/judge/data/code/bin/Release/net8.0/main.dll main -> /home/judge/data/code/bin/Release/net8.0/publish/
ソースコード
using System.ComponentModel; using System.Diagnostics.CodeAnalysis; using System.Numerics; using System.Runtime.CompilerServices; using System.Runtime.InteropServices; using System.Collections; using System.Text; using System.Text.RegularExpressions; using static Tmpl; using static CPDebug; using System.Collections.Specialized; using System.Globalization; using System.Diagnostics; StreamWriter writer = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; //using StreamWriter writer = new StreamWriter(File.Open("turn.txt", FileMode.Create, FileAccess.ReadWrite)); Console.SetOut(writer); //using StreamReader reader = new StreamReader(File.Open("in.txt", FileMode.Open)); //Console.SetIn(reader); Solver.Solve(); Console.Out.Flush(); public static class Solver { private static readonly AtCoderIO cin = new AtCoderIO(); public static long K = 10; public static unsafe void Solve() { long A = cin.Long(); long B = cin.Long(); long C = cin.Long(); long D = cin.Long(); long S = cin.Long(); long T = cin.Long(); long N = cin.Long(); K = cin.Long(); Matrix<ModInt<ModK>> M = new(2); M[0, 0] = A; M[0, 1] = B; M[1, 0] = C; M[1, 1] = D; if (N > 0) M = M.Power(N); else { M[0, 0] = 1; M[0, 1] = 0; M[1, 0] = 0; M[1, 1] = 1; } print($"{S * M[0, 0] + T * M[0, 1]} {S * M[1, 0] + T * M[1, 1]}"); } } public struct ModK : IMod { public long Mod => Solver.K; } public struct Matrix<T> where T : struct, IAdditionOperators<T, T, T>, IMultiplyOperators<T, T, T>, ISubtractionOperators<T, T, T> { private T[,] _data; private int _size; public T this[int r, int c] { get { return _data[r, c]; } set { _data[r, c] = value; } } public T[,] Data => _data; public int Size => _size; public Matrix(int size) { _size = size; _data = new T[size, size]; } public static Matrix<T> operator +(Matrix<T> left, Matrix<T> right) { if (left.Size != right.Size) { throw new InvalidOperationException(); } Matrix<T> dest = new(left.Size); for (int r = 0; r < left.Size; r++) { for (int c = 0; c < left.Size; c++) { dest[r, c] = left[r, c] + right[r, c]; } } return dest; } public static Matrix<T> operator -(Matrix<T> left, Matrix<T> right) { if (left.Size != right.Size) { throw new InvalidOperationException(); } Matrix<T> dest = new(left.Size); for (int r = 0; r < left.Size; r++) { for (int c = 0; c < left.Size; c++) { dest[r, c] = left[r, c] - right[r, c]; } } return dest; } public static Matrix<T> operator *(Matrix<T> left, Matrix<T> right) { if (left.Size != right.Size) { throw new InvalidOperationException(); } Matrix<T> dest = new(left.Size); for (int r = 0; r < dest.Size; r++) { for (int c = 0; c < dest.Size; c++) { for (int i = 0; i < dest.Size; i++) { dest[r, c] += right[i, c] * left[r, i]; } } } return dest; } public Matrix<T> Power(long exp) { if (exp == 1) return this; Matrix<T> half = Power(exp / 2); Matrix<T> res = half * half; if (exp % 2 == 1) res *= this; return res; } public override string ToString() { StringBuilder sb = new(); for (int r = 0; r < _size; r++) { sb.Append('|'); for (int c = 0; c < _size; c++) { sb.Append(_data[r, c]); if (c != _size - 1) { sb.Append(','); sb.Append('\t'); } } sb.Append('|'); sb.Append(Environment.NewLine); } return sb.ToString(); } } public readonly struct Point { public readonly int X; public readonly int Y; public Point(int x, int y) { X = x; Y = y; } public override int GetHashCode() => (X, Y).GetHashCode(); public override string ToString() { return $"({X}, {Y})"; } } public sealed class ReverseComparer<T> : IComparer<T> { public static readonly ReverseComparer<T> Default = new ReverseComparer<T>(Comparer<T>.Default); public static ReverseComparer<T> Reverse(IComparer<T> comparer) { return new ReverseComparer<T>(comparer); } private readonly IComparer<T> comparer = Default; private ReverseComparer(IComparer<T> comparer) { this.comparer = comparer; } public int Compare(T x, T y) { return comparer.Compare(y, x); } } public sealed class AtCoderIO { Queue<string> _readQueue = new Queue<string>(); private void LoadQueue() { if (_readQueue.Count > 0) return; string line = Console.ReadLine(); string[] split = line.Split(' ', StringSplitOptions.RemoveEmptyEntries); for (int i = 0; i < split.Length; i++) _readQueue.Enqueue(split[i]); } private void Guard() { if (_readQueue.Count == 0) { throw new Exception("NO DATA TO READ"); } } public int Int() { LoadQueue(); Guard(); return int.Parse(_readQueue.Dequeue()); } public long Long() { LoadQueue(); Guard(); return long.Parse(_readQueue.Dequeue()); } public string String() { LoadQueue(); Guard(); return _readQueue.Dequeue(); } public short Short() { LoadQueue(); Guard(); return short.Parse(_readQueue.Dequeue()); } public byte Byte() { LoadQueue(); Guard(); return byte.Parse(_readQueue.Dequeue()); } public char Char() { LoadQueue(); Guard(); return char.Parse(_readQueue.Dequeue()); } public double Double() { LoadQueue(); Guard(); return double.Parse(_readQueue.Dequeue()); } public float Float() { LoadQueue(); Guard(); return float.Parse(_readQueue.Dequeue()); } public ModInt<T> ModInt<T>() where T : struct, IMod { return new ModInt<T>(Long()); } public T Read<T>() { Type type = typeof(T); if (type == typeof(int)) return (T)(object)Int(); else if (type == typeof(long)) return (T)(object)Long(); else if (type == typeof(float)) return (T)(object)Float(); else if (type == typeof(double)) return (T)(object)Double(); else if (type == typeof(short)) return (T)(object)Short(); else if (type == typeof(byte)) return (T)(object)Byte(); else if (type == typeof(char)) return (T)(object)Char(); else if (type == typeof(string)) return (T)(object)String(); else return default(T); } public int[] IntArray(int n) { if (n == 0) return Array.Empty<int>(); int[] arr = new int[n]; for (int i = 0; i < n; i++) { arr[i] = Int(); } return arr; } public int[] ZeroIndexedPermutation(int n) { if (n == 0) return Array.Empty<int>(); int[] arr = new int[n]; for (int i = 0; i < n; i++) { arr[i] = Int() - 1; } return arr; } public long[] LongArray(int n) { if (n == 0) return Array.Empty<long>(); long[] arr = new long[n]; for (int i = 0; i < n; i++) { arr[i] = Long(); } return arr; } public double[] DoubleArray(int n) { if (n == 0) return Array.Empty<double>(); double[] arr = new double[n]; for (int i = 0; i < n; i++) { arr[i] = Double(); } return arr; } public ModInt<T>[] ModIntArray<T>(int n) where T : struct, IMod { if (n == 0) return Array.Empty<ModInt<T>>(); ModInt<T>[] arr = new ModInt<T>[n]; for (int i = 0; i < n; i++) { arr[i] = (ModInt<T>)Long(); } return arr; } public T[] ReadArray<T>(int n) { if (n == 0) return Array.Empty<T>(); T[] arr = new T[n]; for (int i = 0; i < n; i++) { arr[i] = Read<T>(); } return arr; } } public static class CPDebug { public static void check<T>(T value, [CallerArgumentExpression(nameof(value))] string name = "value") where T : struct { #if DEBUG Console.Error.WriteLine($"[DEBUG] {name}={value.ToString()}"); #endif } public static void check<T>(IEnumerable<T> value, [CallerArgumentExpression(nameof(value))] string name = "value") { #if DEBUG Console.Error.WriteLine($"[DEBUG] {name}=({string.Join(' ', value)})"); #endif } } public static class Tmpl { public static long pow(long b, long exp) { if (exp == 0) return 1; if (exp == 1) return b; long m = pow(b, exp / 2L); m *= m; if (exp % 2L == 1) m *= b; return m; } public static long modpow(long b, long exp, long mod) { if (exp == 0) return 1; if (exp == 1) return b % mod; long m = modpow(b, exp / 2L, mod); m *= m; m %= mod; if (exp % 2L == 1) m *= b % mod; m %= mod; return m; } static long modinv( long a, long mod ) { long b = mod, u = 1, v = 0; while ( b > 0 ) { long t = a / b; a -= t * b; swap( ref a, ref b ); u -= t * v; swap( ref u, ref v ); } u %= mod; if (u < 0) u += mod; return u; } public static long calcLcm(long a, long b) { return a * b / calcGcd(a, b); } public static long calcGcd(long a, long b) { if (a % b == 0) return b; return calcGcd(b, a % b); } // ax ≡ b (mod m)なる最小のxを求める public static bool solveModLinear(long a, long b, long m, out long minSolution) { long gcd = calcGcd(calcGcd(a, b), m); a /= gcd; b /= gcd; m /= gcd; if (calcGcd(a, m) == 1) { long inv = modinv(a, m); minSolution = (b * inv) % m; return true; } minSolution = 0; return false; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void YesNo(bool t) { Console.WriteLine(t ? "Yes" : "No"); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void YESNO(bool t) { Console.WriteLine(t ? "YES" : "NO"); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void yesno(bool t) { Console.WriteLine(t ? "yes" : "no"); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static bool checkBit(int bit, int n) { return ((1 << n) & bit) != 0; } public static bool nextSubset(ref int set, int super) { set = (set - 1) & super; return set != 0; } public static bool nextCombination(int n, int r, int[] array) { int i = array.Length - 1; while (i >= 0 && array[i] == i + n - r) { i--; } if (i < 0) return false; array[i]++; for (int j = i + 1; j < r; j++) { array[j] = array[j - 1] + 1; } return true; } public static bool nextPermutation<T>(T[] array, int start, int length) where T : IComparable<T> { int end = start + length - 1; if (end <= start) return false; int last = end; while (true) { int pos = last--; if (array[last].CompareTo(array[pos]) < 0) { int i; for (i = end + 1; array[last].CompareTo(array[--i]) >= 0; ) { } T tmp = array[last]; array[last] = array[i]; array[i] = tmp; Array.Reverse(array, pos, end - pos + 1); return true; } if (last == start) { Array.Reverse(array, start, end - start); return false; } } throw new Exception("NextPermutation: Fatal error"); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static bool chmax<T> (ref T target, T value) where T : struct, IComparisonOperators<T, T, bool> { if (value > target) { target = value; return true; } return false; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static bool chmin<T>(ref T target, T value) where T : struct, IComparisonOperators<T, T, bool> { if (value < target) { target = value; return true; } return false; } public static ReadOnlySpan<T> spanOf<T>(List<T> list) { return CollectionsMarshal.AsSpan(list); } public static int lowerBound<T>(T[] array, int start, int end, T value) where T : struct, IComparisonOperators<T, T, bool> { int low = start; int high = end; int mid; while (low < high) { mid = ((high - low) >> 1) + low; if (array[mid] < value) low = mid + 1; else high = mid; } if (low == array.Length - 1 && array[low] < value) { return array.Length; } return low; } public static int lowerBound<T>(List<T> array, int start, int end, T value) where T : struct, IComparisonOperators<T, T, bool> { int low = start; int high = end; int mid; while (low < high) { mid = ((high - low) >> 1) + low; if (array[mid] < value) low = mid + 1; else high = mid; } if (low == array.Count - 1 && array[low] < value) { return array.Count; } return low; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void swap<T>(ref T a, ref T b) where T : struct { T temp = a; a = b; b = temp; } public static int[] compressCoords<T>(T[] a) where T : struct, IComparisonOperators<T, T, bool> { T[] b = a.OrderBy(x => x).Distinct().ToArray(); int[] result = new int[a.Length]; for (int i = 0; i < a.Length; i++) { result[i] = lowerBound(b, 0, b.Length - 1, a[i]); } return result; } public static List<RunLengthElement<T>> compressRunLength<T>(T[] array) where T : struct, IEquatable<T> { List<RunLengthElement<T>> list = new List<RunLengthElement<T>>(); int count = 1; int start = 0; T prev = array[0]; for (int i = 1; i < array.Length; i++) { if (prev.Equals(array[i])) { count++; } else { list.Add(new RunLengthElement<T>(start, count, prev)); start = i; count = 1; } prev = array[i]; } list.Add(new RunLengthElement<T>(start, count, prev)); return list; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void print<T>(IEnumerable<T> array, char delimiter = ' ') { Console.WriteLine(string.Join(delimiter, array)); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void fprint<T>(IEnumerable<T> array, char delimiter = ' ') { print(array); Console.Out.Flush(); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void print(string msg) { Console.WriteLine(msg); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void fprint(string msg) { Console.WriteLine(msg); Console.Out.Flush(); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void print(int val) { print(val.ToString()); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void print(long val) { print(val.ToString()); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void print<T>(ModInt<T> val) where T : struct, IMod { print(val.ToString()); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void fprint(int val) { print(val.ToString()); Console.Out.Flush(); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void fprint(long val) { print(val.ToString()); Console.Out.Flush(); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void fprint<T>(ModInt<T> val) where T : struct, IMod { fprint(val.ToString()); Console.Out.Flush(); } public static void print<T>(T[,] grid) { for (int y = 0; y < grid.GetLength(0); y++) { for (int x = 0; x < grid.GetLength(1); x++) { Console.Write(grid[y, x] + "\t"); } Console.WriteLine(); } } public static void print01(bool t) { Console.WriteLine(t ? "1" : "0"); } public static TSrc lowerBoundKth<TSrc, TCnt>(TSrc min, TSrc max, Func<TSrc, TCnt> f, TCnt bound) where TSrc: struct, INumber<TSrc> where TCnt: struct, INumber<TCnt> { TSrc left = min; TSrc right = max; TSrc two = TSrc.CreateChecked(2); TSrc one = TSrc.CreateChecked(1); while (right > left) { TSrc mid = left + (right - left) / two; TCnt c = f(mid); if (c < bound) { left = mid + one; } else { right = mid; } } return left; } public static bool isSquareNumber(long n) { long q = (long)Math.Floor(Math.Sqrt(n)); return q * q == n; } public static T[][] makeDPTable2D<T>(int length1, int length2, T value) { bool fill = !default(T).Equals(value); T[][] table = new T[length1][]; for (int i = 0; i < length1; i++) { table[i] = new T[length2]; if (fill) { Array.Fill(table[i], value); } } return table; } public static T[][][] makeDPTable3D<T>(int length1, int length2, int length3, T value) { bool fill = !default(T).Equals(value); T[][][] table = new T[length1][][]; for (int i = 0; i < length1; i++) { table[i] = new T[length2][]; for (int j = 0; j < length2; j++) { table[i][j] = new T[length3]; if (fill) { Array.Fill(table[i][j], value); } } } return table; } } public readonly struct RunLengthElement<T> where T : struct { public readonly int Count; public readonly int StartIndex; public readonly T Value; public RunLengthElement(int startIndex, int count, T value) { this.StartIndex = startIndex; this.Count = count; this.Value = value; } } public readonly struct Edge<T> : IEquatable<Edge<T>>, IComparable<Edge<T>> where T : struct, INumber<T> { public readonly int To; public readonly int From; public readonly T Weight; public Edge(int to, T weight) { this.To = to; this.Weight = weight; } public Edge(int from, int to, T weight) { this.To = to; this.From = from; this.Weight = weight; } public override bool Equals(object obj) { if (obj is Edge<T> edge) { return this.Equals(edge); } else { return false; } } public int CompareTo(Edge<T> other) { return Weight.CompareTo(other.Weight); } public bool Equals(Edge<T> edge) { return To == edge.To && From == edge.From && Weight == edge.Weight; } public override int GetHashCode() { return (To, From, Weight).GetHashCode(); } public static bool operator ==(Edge<T> left, Edge<T> right) { return left.Equals(right); } public static bool operator !=(Edge<T> left, Edge<T> right) { return !left.Equals(right); } } /// <summary> /// 自動でmodをとる整数。必要ないならあんまり使いすぎないように。 /// パフォーマンスはあまり良くないかもしれない。 /// </summary> /// <typeparam name="T"></typeparam> public readonly struct ModInt<T> : INumber<ModInt<T>> where T : struct, IMod { public static long Mod => _mod.Mod; private static readonly T _mod = default; public readonly long Value; /// <summary> /// 1を返す。計算量: O(1) /// </summary> public static ModInt<T> One { get; } = CreateFast(1L); /// <summary> /// 0を返す。計算量: O(1) /// </summary> public static ModInt<T> Zero { get; } = CreateFast(0L); public static int Radix => 10; public static ModInt<T> MinValue => CreateFast(0L); public static ModInt<T> MaxValue => CreateFast(_mod.Mod - 1); /// <summary> /// 加法単位元つまり0を返す。計算量: O(1) /// </summary> public static ModInt<T> AdditiveIdentity { get; } = CreateFast(0L); public static ModInt<T> MultiplicativeIdentity { get; } = CreateFast(1L); public ModInt(long value) { Value = SafeMod(value); } private ModInt(long value, bool dummy) { Value = value; } /// <summary> /// modintを構築する。0 <= value < MODのとき限定。速いはず。計算量: O(1) /// </summary> /// <param name="value"></param> /// <returns></returns> [MethodImpl(MethodImplOptions.AggressiveInlining)] public static ModInt<T> CreateFast(long value) { return new ModInt<T>(value, false); } [MethodImpl(MethodImplOptions.AggressiveInlining)] private static long SafeMod(long a) { return a % _mod.Mod + ((a >> 63) & _mod.Mod); } /// <summary> /// exp乗を計算する。計算量: O(log(exp)) /// </summary> /// <param name="exp"></param> /// <returns></returns> public readonly ModInt<T> Power(long exp) { if (exp < 0) { return Power(-exp).Inv(); } else { long res = 1L; long b = Value; while (exp > 0) { if ((exp & 1) == 1) res = res * b % _mod.Mod; b = b * b % _mod.Mod; exp >>= 1; } return CreateFast(res); } } /// <summary> /// 乗法逆元を返す。0は渡さない。計算量: O(logN) /// </summary> /// <returns></returns> public readonly ModInt<T> Inv() { long x = 1, y = 0; long x1 = 0, y1 = 1; long b = _mod.Mod; long a = Value; while (b != 0) { long q = a / b; long t = a % b; a = b; b = t; long tx = x - q * x1; long ty = y - q * y1; x = x1; y = y1; x1 = tx; y1 = ty; } return new(x); } [MethodImpl(256)] public static ModInt<T> operator +(ModInt<T> left, ModInt<T> right) => CreateFast((left.Value + right.Value) % _mod.Mod); [MethodImpl(256)] public static ModInt<T> operator +(ModInt<T> self) => self; [MethodImpl(256)] public static ModInt<T> operator -(ModInt<T> left, ModInt<T> right) => CreateFast((left.Value - right.Value + _mod.Mod) % _mod.Mod); [MethodImpl(256)] public static ModInt<T> operator -(ModInt<T> self) => CreateFast(_mod.Mod - self.Value); [MethodImpl(256)] public static ModInt<T> operator *(ModInt<T> left, ModInt<T> right) => CreateFast(left.Value * right.Value % _mod.Mod); [MethodImpl(256)] public static ModInt<T> operator /(ModInt<T> left, ModInt<T> right) { if (right.Value == 0L) { throw new DivideByZeroException(); } ModInt<T> inv = right.Inv(); return CreateFast(left.Value * inv.Value % _mod.Mod); } public static ModInt<T> operator %(ModInt<T> left, ModInt<T> right) { throw new NotImplementedException(); } public static bool operator <(ModInt<T> left, ModInt<T> right) { throw new NotImplementedException(); } public static bool operator >(ModInt<T> left, ModInt<T> right) { throw new NotImplementedException(); } public static bool operator <=(ModInt<T> left, ModInt<T> right) { throw new NotImplementedException(); } public static bool operator >=(ModInt<T> left, ModInt<T> right) { throw new NotImplementedException(); } [MethodImpl(256)] public static bool operator ==(ModInt<T> left, ModInt<T> right) => left.Value == right.Value; [MethodImpl(256)] public static bool operator !=(ModInt<T> left, ModInt<T> right) => !(left == right); [MethodImpl(256)] public static ModInt<T> operator ++(ModInt<T> self) => CreateFast((self.Value + 1) % _mod.Mod); [MethodImpl(256)] public static ModInt<T> operator --(ModInt<T> self) => CreateFast((self.Value - 1 + _mod.Mod) % _mod.Mod); [MethodImpl(256)] public bool Equals(ModInt<T> other) => Value == other.Value; [MethodImpl(256)] public override bool Equals(object other) { if (other is ModInt<T> m) { return this == m; } else return false; } [MethodImpl(256)] public override int GetHashCode() => Value.GetHashCode(); [MethodImpl(256)] public static implicit operator ModInt<T>(long v) => new ModInt<T>(v); [MethodImpl(256)] public static implicit operator ModInt<T>(int v) => new ModInt<T>(v); [MethodImpl(256)] public static implicit operator long(in ModInt<T> m) => m.Value; [MethodImpl(256)] public static implicit operator int(in ModInt<T> m) => (int)m.Value; public override string ToString() => Value.ToString(); public string ToString(string format, IFormatProvider provider) => Value.ToString(format, provider); #region INumberBase<TSelf> Implementation public static ModInt<T> Abs(ModInt<T> value) => value; public static bool IsCanonical(ModInt<T> value) => true; public static bool IsComplexNumber(ModInt<T> value) => false; public static bool IsFinite(ModInt<T> value) => true; public static bool IsImaginaryNumber(ModInt<T> value) => false; public static bool IsInfinity(ModInt<T> value) => false; public static bool IsInteger(ModInt<T> value) => true; public static bool IsNaN(ModInt<T> value) => false; public static bool IsNegative(ModInt<T> value) => false; public static bool IsPositive(ModInt<T> value) => value.Value != 0L; public static bool IsRealNumber(ModInt<T> value) => true; public static bool IsZero(ModInt<T> value) => value.Value == 0L; public static bool IsEvenInteger(ModInt<T> value) => (value.Value & 1) == 0; public static bool IsOddInteger(ModInt<T> value) => (value.Value & 1) == 1; public static bool IsPositiveInfinity(ModInt<T> value) => false; public static bool IsNegativeInfinity(ModInt<T> value) => false; public static bool IsNormal(ModInt<T> value) => false; public static bool IsSubnormal(ModInt<T> value) => false; public static ModInt<T> MaxMagnitude(ModInt<T> x, ModInt<T> y) { if (x.Value > y.Value) return x; else return y; } public static ModInt<T> MaxMagnitudeNumber(ModInt<T> x, ModInt<T> y) => MaxMagnitude(x, y); public static ModInt<T> MinMagnitude(ModInt<T> x, ModInt<T> y) { if (x.Value < y.Value) return x; else return y; } public static ModInt<T> MinMagnitudeNumber(ModInt<T> x, ModInt<T> y) => MinMagnitude(x, y); public static ModInt<T> CreateChecked<TOther>(TOther value) where TOther : INumberBase<TOther> => new(long.CreateChecked(value)); public static ModInt<T> CreateSaturating<TOther>(TOther value) where TOther : INumberBase<TOther> => new(long.CreateSaturating(value)); public static ModInt<T> CreateTruncating<TOther>(TOther value) where TOther : INumberBase<TOther> => new(long.CreateTruncating(value)); public static ModInt<T> Parse(string s, NumberStyles style, IFormatProvider provider) => Parse(s.AsSpan(), style, provider); public static ModInt<T> Parse(ReadOnlySpan<char> s, NumberStyles style, IFormatProvider provider) => new(long.Parse(s, style, provider)); public static ModInt<T> Parse(ReadOnlySpan<byte> s, NumberStyles style, IFormatProvider provider) => new(long.Parse(s, style, provider)); public static ModInt<T> Parse(string s, IFormatProvider provider) => new(long.Parse(s, provider)); public static ModInt<T> Parse(ReadOnlySpan<char> s, IFormatProvider provider) => new(long.Parse(s, provider)); public bool TryFormat(Span<byte> dest, out int bytesWritten, ReadOnlySpan<char> format, IFormatProvider provider) { return Value.TryFormat(dest, out bytesWritten, format, provider); } public bool TryFormat(Span<char> destination, out int charsWritten, ReadOnlySpan<char> format, IFormatProvider provider) { return Value.TryFormat(destination, out charsWritten, format, provider); } public static bool TryParse(ReadOnlySpan<char> s, NumberStyles style, IFormatProvider provider, out ModInt<T> result) { if (long.TryParse(s, style, provider, out long inner)) { result = new(inner); return true; } else { result = Zero; return false; } } public static bool TryParse(string s, NumberStyles style, IFormatProvider provider, out ModInt<T> result) { if (long.TryParse(s, style, provider, out long inner)) { result = new(inner); return true; } else { result = Zero; return false; } } public static bool TryParse(ReadOnlySpan<char> s, IFormatProvider provider, out ModInt<T> result) { if (long.TryParse(s, provider, out long inner)) { result = new(inner); return true; } else { result = Zero; return false; } } public static bool TryParse(string s, IFormatProvider provider, out ModInt<T> result) { if (long.TryParse(s, provider, out long inner)) { result = new(inner); return true; } else { result = Zero; return false; } } public static bool TryConvertFromChecked<TOther>(TOther value, out ModInt<T> result) where TOther : INumberBase<TOther> { throw new NotImplementedException(); } public static bool TryConvertFromSaturating<TOther>(TOther value, out ModInt<T> result) where TOther : INumberBase<TOther> { throw new NotImplementedException(); } public static bool TryConvertFromTruncating<TOther>(TOther value, [MaybeNullWhen(false)] out ModInt<T> result) where TOther : INumberBase<TOther> { throw new NotImplementedException(); } public static bool TryConvertToChecked<TOther>(ModInt<T> value, [MaybeNullWhen(false)] out TOther result) where TOther : INumberBase<TOther> { throw new NotImplementedException(); } public static bool TryConvertToSaturating<TOther>(ModInt<T> value, [MaybeNullWhen(false)] out TOther result) where TOther : INumberBase<TOther> { throw new NotImplementedException(); } public static bool TryConvertToTruncating<TOther>(ModInt<T> value, [MaybeNullWhen(false)] out TOther result) where TOther : INumberBase<TOther> { throw new NotImplementedException(); } #endregion #region INumber<TSelf> Implementation public int CompareTo(ModInt<T> other) => Value.CompareTo(other.Value); public int CompareTo(object other) => Value.CompareTo(other); #endregion } /// <summary> /// 法を指定するやつ。 /// </summary> public interface IMod { public long Mod { get; } } public readonly struct Mod998244353 : IMod { public long Mod => 998244353L; } public readonly struct Mod1000000007 : IMod { public long Mod => 1000000007L; } public readonly struct Mod897581057 : IMod { public long Mod => 897581057; } public readonly struct Mod880803841 : IMod { public long Mod => 880803841; } public delegate T Monoid<T>(T a, T b); public delegate T Apply<T, M>(T x, M m, int len); /// <summary> /// セグメント木。一応非再帰の実装。 /// </summary> /// <typeparam name="T"></typeparam> public sealed class SegmentTree<T> where T : struct { private int _treeSize; private int _dataSize; private int _originalDataSize; private T[] _data; private Monoid<T> _operator; private Monoid<T> _update; private T _identity; public int OriginalDataSize => _originalDataSize; public int TreeSize => _treeSize; public T Identity => _identity; /// <summary> /// 一点取得。計算量: O(1) /// </summary> /// <param name="index"></param> /// <returns></returns> public T this[int index] { get { return _data[_dataSize - 1 + index]; } } /// <summary> /// 構築する。計算量: O(n) /// </summary> /// <param name="n"></param> /// <param name="op"></param> /// <param name="update"></param> /// <param name="identity"></param> public SegmentTree(int n, Monoid<T> op, Monoid<T> update, T identity) { _originalDataSize = n; int size = 1; while (n > size) { size <<= 1; } _dataSize = size; _treeSize = 2 * size - 1; _data = new T[_treeSize]; Array.Fill(_data, identity); _identity = identity; _operator = op; _update = update; } /// <summary> /// <para>配列から再構築する。計算量: O(n)</para> /// <para>一点更新をn回繰り返すとO(nlogn)となるのでこれを呼んだ方が高速。</para> /// </summary> /// <param name="array"></param> public void Build(T[] array) { for (int i = 0; i < array.Length; i++) { _data[i + _dataSize - 1] = array[i]; } for (int i = _dataSize - 2; i >= 0; i--) { _data[i] = _operator(_data[(i << 1) + 1], _data[(i << 1) + 2]); } } public void UpdateByArray(T[] array) { for (int i = 0; i < array.Length; i++) { _data[i + _dataSize - 1] = _update(_data[i + _dataSize - 1], array[i]); } for (int i = _dataSize - 2; i >= 0; i--) { _data[i] = _operator(_data[(i << 1) + 1], _data[(i << 1) + 2]); } } /// <summary> /// valueで埋める。計算量: O(n) /// </summary> /// <param name="value"></param> public void Fill(T value) { for (int i = 0; i < _originalDataSize; i++) { _data[i + _dataSize - 1] = value; } for (int i = _dataSize - 2; i >= 0; i--) { _data[i] = _operator(_data[(i << 1) + 1], _data[(i << 1) + 2]); } } /// <summary> /// 一点更新する。計算量: O(logn) /// </summary> /// <param name="index"></param> /// <param name="value"></param> public void Update(int index, T value) { index += _dataSize - 1; _data[index] = _update(_data[index], value); while (index > 0) { index = (index - 1) >> 1; _data[index] = _operator(_data[(index << 1) + 1], _data[(index << 1) + 2]); } } /// <summary> /// 区間[l, r)の積を求める。計算量: O(logn) /// </summary> /// <param name="l"></param> /// <param name="r"></param> /// <returns></returns> public T Fold(int l, int r) { l += _dataSize - 1; r += _dataSize - 1; T leftFold = _identity; T rightFold = _identity; while (l < r) { if ((l & 1) == 0) { leftFold = _operator(leftFold, _data[l]); l++; } if ((r & 1) == 0) { r--; rightFold = _operator(_data[r], rightFold); } l = (l - 1) >> 1; r = (r - 1) >> 1; } return _operator(leftFold, rightFold); } /// <summary> /// 中身のspanを返す。計算量: O(1) /// </summary> /// <returns></returns> public ReadOnlySpan<T> AsSpan() { return _data.AsSpan(_dataSize - 1, _originalDataSize); } } // 区間に対する操作と区間に対するクエリを処理する. // 空間計算量: O(4N) // 時間計算量: // - 構築: O(N) // - 操作: O(logN) // - クエリ: O(logN) // - 一点参照: O(logN) // operator: クエリに対応する二項演算をする // mapping: 作用素を作用させる // composition: 作用素を合成する public sealed class LazySegmentTree<T, M> where T : struct, IEquatable<T> where M : struct, IEquatable<M> { private int _treeSize; private int _dataSize; private int _originalDataSize; private T[] _data; private M?[] _lazy; private Monoid<T> _operator; private Apply<T, M> _mapping; private Monoid<M> _composition; private T _identity; public T this[int index] { get { return GetByIndex(index); } } public LazySegmentTree(int n, Monoid<T> op, Apply<T, M> mapping, Monoid<M> composition, T identity) { _originalDataSize = n; int size = 1; while (n > size) { size <<= 1; } _dataSize = size; _treeSize = 2 * size - 1; _data = new T[_treeSize]; _data.AsSpan().Fill(_identity); _lazy = new M?[_treeSize]; _identity = identity; _operator = op; _mapping = mapping; _composition = composition; } public void Build(T[] array) { for (int i = 0; i < array.Length; i++) { _data[i + _dataSize - 1] = array[i]; } for (int i = _dataSize - 2; i >= 0; i--) { _data[i] = _operator(_data[(i << 1) + 1], _data[(i << 1) + 2]); } } private void Evaluate(int index, int l, int r) { if (_lazy[index] is null) { return; } if (index < _dataSize - 1) { _lazy[(index << 1) + 1] = GuardComposition(_lazy[(index << 1) + 1], _lazy[index]); _lazy[(index << 1) + 2] = GuardComposition(_lazy[(index << 1) + 2], _lazy[index]); } _data[index] = _mapping(_data[index], (M)_lazy[index], r - l); _lazy[index] = null; } private M GuardComposition(M? a, M? b) { if (a is null) { return (M)b; } else { return _composition((M)a, (M)b); } } private void ApplyRec(int a, int b, M m, int index, int l, int r) { Evaluate(index, l, r); if (a >= r || b <= l) { return; } if (a <= l && r <= b) { _lazy[index] = GuardComposition(_lazy[index], m); Evaluate(index, l, r); } else { ApplyRec(a, b, m, (index << 1) + 1, l, (l + r) / 2); ApplyRec(a, b, m, (index << 1) + 2, (l + r) / 2, r); _data[index] = _operator(_data[(index << 1) + 1], _data[(index << 1) + 2]); } } public void Apply(int left, int right, M m) { ApplyRec(left, right, m, 0, 0, _dataSize); } public T Query(int left, int right) { return QueryRec(left, right, 0, 0, _dataSize); } private T QueryRec(int left, int right, int index, int nodeLeft, int nodeRight) { Evaluate(index, nodeLeft, nodeRight); if (left >= nodeRight || right <= nodeLeft) { return _identity; } if (left <= nodeLeft && nodeRight <= right) { return _data[index]; } T leftChild = QueryRec(left, right, (index << 1) + 1, nodeLeft, (nodeLeft + nodeRight) >> 1); T rightChild = QueryRec(left, right, (index << 1) + 2, (nodeLeft + nodeRight) >> 1, nodeRight); return _operator(leftChild, rightChild); } public T GetByIndex(int target) { if (target < 0 || target >= _originalDataSize) { throw new Exception("Index is out of range."); } return AccessRec(target, 0, 0, _dataSize); } private T AccessRec(int target, int index, int l, int r) { Evaluate(index, l, r); if (index >= _dataSize - 1) { return _data[index]; } int mid = (l + r) / 2; if (target < mid) { return AccessRec(target, (index << 1) + 1, l, mid); } else { return AccessRec(target, (index << 1) + 2, mid, r); } } // index以下のノードをすべて即時に評価する. private void EvaluateAll(int index, int l, int r) { if (_lazy[index] is null) { if (index < _dataSize - 1) { EvaluateAll((index << 1) + 1, l, (l + r) / 2); EvaluateAll((index << 1) + 2, (l + r) / 2, r); } return; } if (index < _dataSize - 1) { _lazy[(index << 1) + 1] = GuardComposition(_lazy[(index << 1) + 1], _lazy[index]); _lazy[(index << 1) + 2] = GuardComposition(_lazy[(index << 1) + 2], _lazy[index]); EvaluateAll((index << 1) + 1, l, (l + r) / 2); EvaluateAll((index << 1) + 2, (l + r) / 2, r); } _data[index] = _mapping(_data[index], (M)_lazy[index], r - l); _lazy[index] = null; } // 返されたArraySegment<T>は変更してはいけない. public ArraySegment<T> GetData() { EvaluateAll(0, 0, _dataSize); return new ArraySegment<T>(_data, _dataSize - 1, _originalDataSize); } } public static class SegmentTreeBuilder { public static LazySegmentTree<T, T> RangeAddMax<T>(int n, T identity) where T : struct, INumber<T> { return new LazySegmentTree<T, T>(n, T.Max, (x, m, l) => { return x + m; }, (a, b) => { return a + b; }, identity); } public static LazySegmentTree<T, T> RangeUpdateMax<T>(int n, T identity) where T : struct, INumber<T> { return new LazySegmentTree<T, T>(n, T.Max, (x, m, l) => { return m; }, (x, y) => { return y; }, identity); } public static LazySegmentTree<T, T> RangeAddMin<T>(int n, T identity) where T : struct, INumber<T> { return new LazySegmentTree<T, T>(n, T.Min, (x, m, l) => { return x + m; }, (a, b) => { return a + b; }, identity); } public static LazySegmentTree<T, T> RangeUpdateMin<T>(int n, T identity) where T : struct, INumber<T> { return new LazySegmentTree<T, T>(n, T.Min, (x, m, l) => { return m; }, (x, y) => { return y; }, identity); } public static LazySegmentTree<T, T> RangeAddSum<T>(int n, T identity) where T : struct, INumber<T> { return new LazySegmentTree<T, T>(n, (x, y) => x + y, (x, m, l) => { return x + m * T.CreateChecked(l); }, (a, b) => { return a + b; }, identity); } public static LazySegmentTree<T, T> RangeUpdateSum<T>(int n, T identity) where T : struct, INumber<T> { return new LazySegmentTree<T, T>(n, (x, y) => x + y, (x, m, l) => { return m * T.CreateChecked(l); }, (a, b) => { return b; }, identity); } public static SegmentTree<T> PointUpdateMax<T>(int n, T identity) where T : struct, INumber<T> { return new SegmentTree<T>(n, T.Max, (a, b) => b, identity); } public static SegmentTree<T> PointAddMax<T>(int n, T identity) where T : struct, INumber<T> { return new SegmentTree<T>(n, T.Max, (a, b) => a + b, identity); } public static SegmentTree<T> PointUpdateMin<T>(int n, T identity) where T : struct, INumber<T> { return new SegmentTree<T>(n, T.Min, (a, b) => b, identity); } public static SegmentTree<T> PointAddMin<T>(int n, T identity) where T : struct, INumber<T> { return new SegmentTree<T>(n, T.Min, (a, b) => a + b, identity); } public static SegmentTree<T> PointUpdateSum<T>(int n, T identity) where T : struct, INumber<T> { return new SegmentTree<T>(n, (x, y) => x + y, (a, b) => b, identity); } public static SegmentTree<T> PointAddSum<T>(int n, T identity) where T : struct, INumber<T> { return new SegmentTree<T>(n, (x, y) => x + y, (a, b) => a + b, identity); } } public sealed class PrefixSum2D<T> where T : struct, IAdditionOperators<T, T, T>, ISubtractionOperators<T, T, T> { private T[,] _sums; public PrefixSum2D(T[,] sequence) { int height = sequence.GetLength(0); int width = sequence.GetLength(1); _sums = new T[height + 1, width + 1]; // build prefix sum for (int y = 0; y < height; y++) { for (int x = 0; x < width; x++) { _sums[y + 1, x + 1] = _sums[y + 1, x] + _sums[y, x + 1] - _sums[y, x] + sequence[y, x]; } } } public T Sum(int startInclX, int startInclY, int endExclX, int endExclY) { return _sums[endExclY, endExclX] + _sums[startInclY, startInclX] - _sums[startInclY, endExclX] - _sums[endExclY, startInclX]; } public T AllSum() { return _sums[_sums.GetLength(0) - 1, _sums.GetLength(1) - 1]; } } public sealed class PrefixSum<T> where T : struct, IAdditionOperators<T, T, T>, ISubtractionOperators<T, T, T>, IAdditiveIdentity<T, T> { private T[] _sums; public PrefixSum(T[] sequence) { _sums = new T[sequence.Length + 1]; _sums[0] = T.AdditiveIdentity; for (int i = 0; i < sequence.Length; i++) { _sums[i + 1] = _sums[i] + sequence[i]; } } // [a, b) public T Sum(int aIncl, int bExcl) { return _sums[bExcl] - _sums[aIncl]; } public T AllSum() { return _sums[^1]; } public T[] GetArray() { return _sums; } } public sealed class UnionFind { private int[] _parents; private int[] _size; private int _vertexCount; public int VertexCount => _vertexCount; public UnionFind(int n) { _vertexCount = n; _parents = new int[n]; _size = new int[n]; for (int i = 0; i < n; i++) { _parents[i] = i; _size[i] = 1; } } public int Root(int x) { if (_parents[x] == x) return x; return _parents[x] = Root(_parents[x]); } public void Unite(int x, int y) { int rootX = Root(x); int rootY = Root(y); if (rootX == rootY) return; int from = rootX; int to = rootY; // merge from to to if (_size[from] > _size[to]) { (from, to) = (to, from); } _size[to] += _size[from]; _parents[from] = to; } public List<int> Find(int x) { int rootX = Root(x); List<int> set = new List<int>(); for (int i = 0; i < _vertexCount; i++) { if (Root(i) == rootX) set.Add(i); } return set; } public Dictionary<int, List<int>> FindAll() { Dictionary<int, List<int>> sets = new Dictionary<int, List<int>>(); for (int i = 0; i < _vertexCount; i++) { int root = Root(i); if (sets.ContainsKey(root)) sets[root].Add(i); else sets[root] = new List<int>() { i }; } return sets; } public bool Same(int x, int y) { int rootX = Root(x); int rootY = Root(y); return rootX == rootY; } public int Size(int v) { return _size[Root(v)]; } public void Clear() { for (int i = 0; i < _vertexCount; i++) { _parents[i] = i; } } }