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 unsafe void Solve() { int N = cin.Int(); int F = cin.Int(); int[] A = cin.IntArray(N); int[] B = cin.IntArray(N); int[] C = cin.IntArray(N); int max = F * N; bool[] dp = new bool[max + 1]; bool[] nextdp = new bool[max + 1]; dp[A[0]] = true; dp[B[0]] = true; dp[C[0]] = true; int one = 0; for (int i = 0; i < max; i++) { if (dp[i]) one++; } print(one); for (int i = 2; i <= N; i++) { int ans = 0; for (int j = 0; j <= max; j++) { if (j >= A[i - 1]) { nextdp[j] |= dp[j - A[i - 1]]; } if (j >= B[i - 1]) { nextdp[j] |= dp[j - B[i - 1]]; } if (j >= C[i - 1]) { nextdp[j] |= dp[j - C[i - 1]]; } if (nextdp[j]) ans++; } print(ans); (dp, nextdp) = (nextdp, dp); } } } public struct Vector<T> where T : struct, INumber<T> { private T[] _data; private int _size; public T this[int index] { get => _data[index]; set => _data[index] = value; } public int Size => _size; public T[] Data => _data; public Vector(int size) { _data = new T[size]; _size = size; } } public struct Matrix<T> where T : struct, INumber<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 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(); } } static class Constants { public const long Mod = 998244353L; //public const long Mod = 10007L; //public const long Mod = 1000000007L; } 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 ModInt() { return new ModInt(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 if (type == typeof(ModInt)) return (T)(object)ModInt(); 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[] ModIntArray(int n) { if (n == 0) return Array.Empty<ModInt>(); ModInt[] arr = new ModInt[n]; for (int i = 0; i < n; i++) { arr[i] = (ModInt)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") { #if DEBUG Console.WriteLine($"[DEBUG] {name}={value.ToString()}"); #endif } public static void check<T>(IEnumerable<T> value, [CallerArgumentExpression(nameof(value))] string name = "value") { #if DEBUG Console.WriteLine($"[DEBUG] {name}=({string.Join(' ', value)})"); #endif } } public static class Tmpl { public static int combination(int n, int r) { int c = 1; for (int i = 1; i <= r; i++) { c = c * (n - i + 1) / i; } return c; } public static long combination(long n, long r) { long c = 1; for (long i = 1; i <= r; i++) { c = c * (n - i + 1) / i; } return c; } 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 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"); } public static unsafe Dictionary<char, int> cntCharOcc(string s) { Dictionary<char, int> dict = new Dictionary<char, int>(); fixed (char* ptr = s) { for (int i = 0; i < s.Length; i++) { if (dict.ContainsKey(ptr[i])) { dict[ptr[i]] += 1; } else { dict[ptr[i]] = 1; } } } return dict; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void chmax<T> (ref T target, T value) where T : struct, IComparisonOperators<T, T, bool> { if (value > target) { target = value; } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void chmin<T>(ref T target, T value) where T : struct, IComparisonOperators<T, T, bool> { if (value < target) { target = value; } } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void arrMod<T>(T[] array, T b) where T : IModulusOperators<T, T, T> { for (int i = 0; i < array.Length; i++) { array[i] %= b; } } public static ReadOnlySpan<T> spanOf<T>(List<T> list) { return CollectionsMarshal.AsSpan(list); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void swap<T>(T[] array, int i, int j) where T : struct { (array[i], array[j]) = (array[j], array[i]); } public static void shuffle<T>(T[] array) where T : struct { Random random = new Random(); for (int i = array.Length - 1; i > 0; i--) { int index = random.Next(0, i + 1); swap(array, index, i); } } 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; } public static int upperBound<T>(T[] array, T value) where T : struct, IComparisonOperators<T, T, bool> { var l = 0; var r = array.Length - 1; while (l <= r) { var mid = l + (r - l) / 2; if (array[mid] <= value) l = mid + 1; else r = mid - 1; } return l; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static void swap<T>(ref T a, ref T b) where T : struct { T temp = a; a = b; b = temp; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static bool dbleq(double a, double b) { return Math.Abs(a - b) < double.Epsilon; } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static int dblAsInt(double d) { return (int)Math.Round(d, 0); } [MethodImpl(MethodImplOptions.AggressiveInlining)] public static long dblAsLong(double d) { return (long)Math.Round(d, 0); } 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; } public static char[] alphabetsLower() { return new[] { 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z' }; } public static char[] alphebetsUpper() { return new[]{ 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'}; } [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(ModInt val) { 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(ModInt val) { 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 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); } } public readonly struct ModInt : IEquatable<ModInt> { private readonly long Value; public static ModInt One => (ModInt)1L; public static ModInt Zero => (ModInt)0L; public ModInt(long value) { Value = SafeMod(value); } [MethodImpl(MethodImplOptions.AggressiveInlining)] private static long SafeMod(long a) { a %= Constants.Mod; if (a < 0) a += Constants.Mod; return a; } public ModInt Power(long exp) { if (exp <= -1) return this; if (exp == 0) return 1; if (exp == 1) return this; ModInt m = Power(exp / 2); m *= m; if (exp % 2 == 1) m *= this; return m; } public ModInt Inv() { return this.Power(Constants.Mod - 2L); } public static ModInt operator +(ModInt left, ModInt right) { return new ModInt(SafeMod(left.Value + right.Value)); } public static ModInt operator -(ModInt left, ModInt right) { return new ModInt(SafeMod(left.Value - right.Value)); } public static ModInt operator *(ModInt left, ModInt right) { return new ModInt(SafeMod(left.Value * right.Value)); } public static ModInt operator /(ModInt left, ModInt right) { if (right.Value == 0L) { return Zero; } ModInt inv = right.Inv(); return SafeMod(left * inv); } public static ModInt operator %(ModInt left, ModInt right) { if (right.Value == 0L) { return Zero; } return new ModInt(SafeMod(left.Value % right.Value)); } public static bool operator ==(ModInt left, ModInt right) { return left.Value == right.Value; } public static bool operator != (ModInt left, ModInt right) { return !(left == right); } public bool Equals(ModInt other) { return Value == other.Value; } public override bool Equals(object other) { if (other is ModInt m) { return this == m; } else return false; } public override int GetHashCode() { return Value.GetHashCode(); } public static implicit operator ModInt(long v) { return new ModInt(v); } public static implicit operator ModInt(int v) { return new ModInt(v); } public static implicit operator long(ModInt m) { return m.Value; } public static implicit operator int(ModInt m) { return (int)m.Value; } public long Raw() => Value; public override string ToString() { return Value.ToString(); } } public delegate T Monoid<T>(T a, T b); public delegate T Apply<T, M>(T x, M m, int len); // 一点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(2N) // 時間計算量: // - 構築: O(N) // - 操作: O(logN) // - クエリ: O(logN) 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> _apply; private T _identity; public int OriginalDataSize => _originalDataSize; public int TreeSize => _treeSize; public T Identity => _identity; public T this[int index] { get { return _data[_dataSize - 1 + index]; } } public SegmentTree(int n, Monoid<T> op, Monoid<T> apply, T identity) { _originalDataSize = n; int size = 1; while (n > size) { size <<= 1; } _dataSize = size; _treeSize = 2 * size - 1; _data = new T[_treeSize]; _identity = identity; _operator = op; _apply = apply; } 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 Apply(int index, T value) { index += _dataSize - 1; _data[index] = _apply(_data[index], value); while (index > 0) { index = (index - 1) >> 1; _data[index] = _operator(_data[(index << 1) + 1], _data[(index << 1) + 2]); } } 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) { 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); } // 返されたArraySegment<T>は変更してはいけない. public ArraySegment<T> GetData() { return new ArraySegment<T>(_data, _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 <= l && r <= b) { _lazy[index] = GuardComposition(_lazy[index], m); Evaluate(index, l, r); } else if (a < r && l < b) { 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 struct BeatsNode<T> where T : struct, IEquatable<T> { public T Value; public bool Failed; public BeatsNode(T value) { Failed = false; Value = value; } } // 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: (操作に依存した計算量) // - クエリ: O(logN) // operator: クエリに対応する二項演算をする. 必ず計算ができる必要がある. // mapping: 作用素を作用させる. 計算が出来なければFailed←trueとして返す. この際, 子ノードに対する評価が実行される. // composition: 作用素を合成する public sealed class SegmentTreeBeats<T, M> where T : struct, IEquatable<T> where M : struct, IEquatable<M> { private int _treeSize; private int _dataSize; private int _originalDataSize; private BeatsNode<T>[] _data; private M?[] _lazy; private Monoid<BeatsNode<T>> _operator; private Apply<BeatsNode<T>, M> _mapping; private Monoid<M> _composition; private T _identity; private BeatsNode<T> _identityNode; public T this[int index] { get{ return GetByIndex(index); } } public SegmentTreeBeats(int n, Monoid<BeatsNode<T>> op, Apply<BeatsNode<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 BeatsNode<T>[_treeSize]; _identityNode = new BeatsNode<T>(_identity); _data.AsSpan().Fill(_identityNode); _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] = new BeatsNode<T>(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]); if (_lazy[(index << 1) + 1] is not null) { Evaluate((index << 1) + 1, l, (l + r) / 2); } _lazy[(index << 1) + 1] = _lazy[index]; if (_lazy[(index << 1) + 2] is not null) { Evaluate((index << 1) + 2, (l + r) / 2, r); } _lazy[(index << 1) + 2] = _lazy[index]; } //_data[index] = _mapping(_data[index], (M)_lazy[index], r - l); // 計算してみる BeatsNode<T> val = _mapping(_data[index], (M)_lazy[index], r - l); // 計算出来なければ if (val.Failed) { if (index >= _dataSize - 1) { throw new Exception("葉ノードに対するmappingは失敗してはいけません"); } // 子ノードを即評価 Evaluate((index << 1) + 1, l, (l + r) / 2); Evaluate((index << 1) + 2, (l + r) / 2, r); // 子ノードの結果から親を更新 _data[index] = _operator(_data[(index << 1) + 1], _data[(index << 1) + 2]); } else { // 計算できればそのまま更新 _data[index] = val; } _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 <= l && r <= b) { _lazy[index] = GuardComposition(_lazy[index], m); Evaluate(index, l, r); } else if (a < r && l < b) { 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).Value; } private BeatsNode<T> QueryRec(int left, int right, int index, int nodeLeft, int nodeRight) { Evaluate(index, nodeLeft, nodeRight); if (left >= nodeRight || right <= nodeLeft) { return _identityNode; } if (left <= nodeLeft && nodeRight <= right) { return _data[index]; } BeatsNode<T> leftChild = QueryRec(left, right, (index << 1) + 1, nodeLeft, (nodeLeft + nodeRight) >> 1); BeatsNode<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].Value; } 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]); if (_lazy[(index << 1) + 1] is not null) { Evaluate((index << 1) + 1, l, (l + r) / 2); } _lazy[(index << 1) + 1] = _lazy[index]; if (_lazy[(index << 1) + 2] is not null) { Evaluate((index << 1) + 2, (l + r) / 2, r); } _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 void GetData(T[] destination) { if (destination.Length < _originalDataSize) { throw new Exception("書き込み先配列の大きさが足りない"); } EvaluateAll(0, 0, _dataSize); //return new ArraySegment<T>(_data, _dataSize - 1, _originalDataSize); for (int i = 0; i < _originalDataSize; i++) { destination[i] = _data[_dataSize - 1 + i].Value; } } } public struct ChangeNode<T> : IEquatable<ChangeNode<T>> where T : struct, INumber<T>, IMinMaxValue<T> { public T Max; public int MaxCount; public T SecondMax; public T Min; public int MinCount; public T SecondMin; public T Sum; public bool Equals(ChangeNode<T> other) { return this.Equals(other); } public static ChangeNode<R> MakeLeaf<R>(R value) where R : struct, INumber<R>, IMinMaxValue<R> { return new ChangeNode<R>() { Max = value, MaxCount = 1, SecondMax = R.MinValue, Min = value, MinCount = 1, SecondMin = R.MaxValue, Sum = value }; } } 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; } } } public sealed class RollbackUnionFind { private int[] _data; private Stack<(int, int)> _history; int _innerSnap; public RollbackUnionFind(int n) { _innerSnap = 0; _data = new int[n]; Array.Fill(_data, -1); _history = new Stack<(int, int)>(); } public bool Unite(int x, int y) { x = Find(x); y = Find(y); _history.Push((x, _data[x])); _history.Push((y, _data[y])); if (x == y) return false; if (_data[x] > _data[y]) { swap(ref x, ref y); } _data[x] += _data[y]; _data[y] = x; return true; } public int Find(int k) { if (_data[k] < 0) return k; return Find(_data[k]); } public bool Same(int x, int y) { return Find(x) == Find(y); } public int Size(int k) { return -_data[Find(k)]; } public void Undo() { _data[_history.Peek().Item1] = _history.Peek().Item2; _history.Pop(); _data[_history.Peek().Item1] = _history.Peek().Item2; _history.Pop(); } public void Snapshot() { _innerSnap = _history.Count >> 1; } public int GetState() { return _history.Count >> 1; } public void Rollback(int state = -1) { if (state == -1) state = _innerSnap; state <<= 1; while (state < _history.Count) this.Undo(); } } public sealed class Imos<T> where T : struct, IAdditionOperators<T, T, T>, ISubtractionOperators<T, T, T> { private T[] _data; public Imos(T[] array) { _data = array; } public Imos(int len) { _data = new T[len]; } public void AddQueryLen(int start, int length, T value) { this.AddQuery(start, start + length, value); } public void AddQuery(int start, int end, T value) { _data[start] += value; if (end < _data.Length) { _data[end] -= value; } } public void Simulate() { for (int i = 1; i < _data.Length; i++) { _data[i] += _data[i - 1]; } } public T[] GetData() { return _data; } } public sealed class Imos2D<T> where T : struct, IAdditionOperators<T, T, T>, ISubtractionOperators<T, T, T> { private T[,] _data; private int _width; private int _height; public Imos2D(T[,] data) { _data = data; _width = data.GetLength(1); _height = data.GetLength(0); } public Imos2D(int h, int w) { _data = new T[h, w]; _width = w; _height = h; } public void AddQuery(int startX, int startY, int endX, int endY, T value) { _data[startY, startX] += value; if (endX < _width) { _data[startY, endX] -= value; } if (endY < _height) { _data[endY, startX] -= value; } if (endX < _width && endY < _height) { _data[endY, endX] += value; } } public void AddQueryLen(int x, int y, int w, int h, T value) { this.AddQuery(x, y, x + w, y + h, value); } public void Simulate() { for (int x = 1; x < _width; x++) { for (int y = 0; y < _height; y++) { _data[y, x] += _data[y, x - 1]; } } for (int y = 1; y < _height; y++) { for (int x = 0; x < _width; x++) { _data[y, x] += _data[y - 1, x]; } } } public T[,] GetData() { return _data; } } public static class LIS { // NOTE: 空間計算量O(max), 時間計算量O(nlogn) public static int LengthOfLIS(int[] sequence, int max) { if (max >= 1_000_000_00) { throw new ArgumentException("Max value is too large.", nameof(max)); } var seg = SegmentTreeBuilder.PointUpdateMax<int>(max + 1, 0); for (int i = 1; i <= sequence.Length; i++) { int m = seg.Query(0, sequence[i - 1]); seg.Apply(sequence[i - 1], m + 1); } return seg.Query(0, max + 1); } } public static class TestCase { private static Random _random = new Random(); public static void Seed(int seed) { _random = new Random(seed); } public static string RandomStringLower(int length) { Span<char> span = stackalloc char[length]; for (int i = 0; i < length; i++) { char ch = (char)('a' + _random.Next(0, 26)); span[i] = ch; } return new string(span); } public static string RandomStringUpper(int length) { return RandomStringLower(length).ToUpperInvariant(); } public static int[] RandomPermutation(int length) { int[] d = new int[length]; for (int i = 0; i < length; i++) d[i] = i + 1; shuffle(d); return d; } public static long[] RandomArrayLong(int length, long min, long max) { long[] d = new long[length]; for (int i = 0; i < length; i++) { d[i] = _random.NextInt64(min, max + 1); } return d; } public static int[] RandomArray(int length, int min, int max) { int[] d = new int[length]; for (int i = 0; i < length; i++) { d[i] = _random.Next(min, max + 1); } return d; } public static int[,] Random2DArray(int height, int width, int min, int max) { int[,] d = new int[height, width]; for (int y = 0; y < height; y++) { for (int x = 0; x < width; x++) { d[y, x] = _random.Next(min, max + 1); } } return d; } public static long[,] Random2DArrayLong(int height, int width, int min, int max) { long[,] d = new long[height, width]; for (int y = 0; y < height; y++) { for (int x = 0; x < width; x++) { d[y, x] = _random.NextInt64(min, max + 1); } } return d; } public static char[,] RandomCharGrid(int height, int width, params char[] tiles) { char[,] d = new char[height, width]; for (int y = 0; y < height; y++) { for (int x = 0; x < width; x++) { d[y, x] = tiles[_random.Next(0, tiles.Length)]; } } return d; } } public sealed class NumberUtility { private bool[] _isPrime; private int[] _minFactor; private int[] _mobius; private int _n; public NumberUtility(int max) { _n = max; _isPrime = new bool[max + 1]; _minFactor = new int[max + 1]; _mobius = new int[max + 1]; Array.Fill(_isPrime, true); Array.Fill(_minFactor, -1); Array.Fill(_mobius, 1); _isPrime[1] = false; _minFactor[1] = 1; for (int i = 2; i <= _n; i++) { if (!_isPrime[i]) continue; _minFactor[i] = i; _mobius[i] = -1; for (int j = i + i; j <= _n; j += i) { _isPrime[j] = false; if (_minFactor[j] == -1) _minFactor[j] = i; if (j / i % i == 0) _mobius[j] = 0; else _mobius[j] = -_mobius[j]; } } } public int Mu(int n) { return _mobius[n]; } public int MinFactor(int n) { return _minFactor[n]; } public bool IsPrime(int n) { return _isPrime[n]; } } public sealed class Convolution { private readonly long _mod; public Convolution(long mod) { _mod = mod; } public List<long> CalcConvolution(List<long> a, List<long> b) { return null; } }