Problem:
Score : 100 points

Problem Statement

You are given two integer arrays a_0, a_1, ..., a_{N - 1} and b_0, b_1, ..., b_{M - 1}. Calculate the array c_0, c_1, ..., c_{(N - 1) + (M - 1)}, defined by c_i = \sum_{j = 0}^i a_j b_{i - j} \bmod 998244353.

Constraints

1 \leq N, M \leq 524288

0 \leq a_i, b_i < 998244353

All values in Input are integer.

Input

Input is given from Standard Input in the following format:

N M
a_0 a_1 ... a_{N-1}
b_0 b_1 ... b_{M-1}

Output

Print the answer in the following format:

c_0 c_1 ... c_{(N - 1) + (M - 1)}

Sample Input 1

4 5
1 2 3 4
5 6 7 8 9

Sample Output 1

5 16 34 60 70 70 59 36

Sample Input 2

1 1
10000000
10000000

Sample Output 2

871938225

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

#region いつもの
using AtCoderProject;
using System;
using System.Collections.Generic;
using System.Linq;
using static AtCoderProject.Global;
using BigInteger = System.Numerics.BigInteger;
using BitOperations = System.Numerics.BitOperations;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using StringBuilder = System.Text.StringBuilder;
using Unsafe = System.Runtime.CompilerServices.Unsafe;

namespace AtCoderProject { using System.IO; using System.Text; using System.Diagnostics; using System.Runtime.CompilerServices; using System.Linq.Expressions; public static class Global { public static int Gcd(params int[] nums) { var gcd = nums[0]; for (var i = 1; i < nums.Length; i++) gcd = Gcd(nums[i], gcd); return gcd; } public static int Gcd(int a, int b) => b > a ? Gcd(b, a) : (b == 0 ? a : Gcd(b, a % b)); public static int Lcm(int a, int b) => a / Gcd(a, b) * b; public static int Lcm(params int[] nums) { var lcm = nums[0]; for (var i = 1; i < nums.Length; i++) lcm = Lcm(lcm, nums[i]); return lcm; } public static long Gcd(params long[] nums) { var gcd = nums[0]; for (var i = 1; i < nums.Length; i++) gcd = Gcd(nums[i], gcd); return gcd; } public static long Gcd(long a, long b) => b > a ? Gcd(b, a) : (b == 0 ? a : Gcd(b, a % b)); public static long Lcm(long a, long b) => a / Gcd(a, b) * b; public static long Lcm(params long[] nums) { var lcm = nums[0]; for (var i = 1; i < nums.Length; i++) lcm = Lcm(lcm, nums[i]); return lcm; } public static T[] NewArray<T>(int len0, T value) => new T[len0].Fill(value); public static T[] NewArray<T>(int len0, Func<T> factory) { var arr = new T[len0]; for (int i = 0; i < arr.Length; i++) arr[i] = factory(); return arr; } public static T[][] NewArray<T>(int len0, int len1, T value) where T : struct { var arr = new T[len0][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, value); return arr; } public static T[][] NewArray<T>(int len0, int len1, Func<T> factory) { var arr = new T[len0][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, factory); return arr; } public static T[][][] NewArray<T>(int len0, int len1, int len2, T value) where T : struct { var arr = new T[len0][][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, value); return arr; } public static T[][][] NewArray<T>(int len0, int len1, int len2, Func<T> factory) { var arr = new T[len0][][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, factory); return arr; } public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, T value) where T : struct { var arr = new T[len0][][][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, value); return arr; } public static T[][][][] NewArray<T>(int len0, int len1, int len2, int len3, Func<T> factory) { var arr = new T[len0][][][]; for (int i = 0; i < arr.Length; i++) arr[i] = NewArray(len1, len2, len3, factory); return arr; } public static long Pow(long x, int y) { long res = 1; for (; y > 0; y >>= 1) { if ((y & 1) == 1) res *= x; x *= x; } return res; } public static BigInteger ParseBigInteger(ReadOnlySpan<char> s) { /* 自前実装の方が速い */ if (s[0] == '-') return -ParseBigInteger(s[1..]); BigInteger res; if (s.Length % 9 == 0) res = 0; else { res = new BigInteger(int.Parse(s.Slice(0, s.Length % 9))); s = s.Slice(s.Length % 9); } while (s.Length > 0) { var sp = s.Slice(0, 9); res *= 1000_000_000; res += int.Parse(sp); s = s.Slice(9); } return res; } public static int PopCount(int x) => BitOperations.PopCount((uint)x); public static int PopCount(long x) => BitOperations.PopCount((ulong)x); public static int PopCount(ulong x) => BitOperations.PopCount(x); public static int MSB(int x) => BitOperations.Log2((uint)x); public static int MSB(uint x) => BitOperations.Log2(x); public static int MSB(long x) => BitOperations.Log2((ulong)x); public static int MSB(ulong x) => BitOperations.Log2(x); public static int LSB(int x) => BitOperations.TrailingZeroCount((uint)x); public static int LSB(uint x) => BitOperations.TrailingZeroCount(x); public static int LSB(long x) => BitOperations.TrailingZeroCount((ulong)x); public static int LSB(ulong x) => BitOperations.TrailingZeroCount(x); } public static class Ext { public static bool UpdateMax<T>(this ref T r, T val) where T : struct, IComparable<T> { if (r.CompareTo(val) < 0) { r = val; return true; } return false; } public static bool UpdateMin<T>(this ref T r, T val) where T : struct, IComparable<T> { if (r.CompareTo(val) > 0) { r = val; return true; } return false; } public static T[] Fill<T>(this T[] arr, T value) { Array.Fill(arr, value); return arr; } public static T[] Sort<T>(this T[] arr) { Array.Sort(arr); return arr; } public static string[] Sort(this string[] arr) => Sort(arr, StringComparer.Ordinal); public static T[] Sort<T, U>(this T[] arr, Expression<Func<T, U>> selector) where U : IComparable<U> => Sort(arr, ExComparer<T>.CreateExp(selector)); public static T[] Sort<T>(this T[] arr, Comparison<T> comparison) { Array.Sort(arr, comparison); return arr; } public static T[] Sort<T>(this T[] arr, IComparer<T> comparer) { Array.Sort(arr, comparer); return arr; } public static T[] Reverse<T>(this T[] arr) { Array.Reverse(arr); return arr; } public static (int index, T max) MaxBy<T>(this T[] arr) where T : IComparable<T> { T max = arr[0]; int maxIndex = 0; for (int i = 0; i < arr.Length; i++) { if (max.CompareTo(arr[i]) < 0) { max = arr[i]; maxIndex = i; } } return (maxIndex, max); } public static (int index, T max) MaxBy<T, TMax>(this T[] arr, Func<T, TMax> maxBySelector) where TMax : IComparable<TMax> { var maxItem = maxBySelector(arr[0]); var max = arr[0]; int maxIndex = 0; for (int i = 0; i < arr.Length; i++) { var nx = maxBySelector(arr[i]); if (maxItem.CompareTo(nx) < 0) { maxItem = nx; max = arr[i]; maxIndex = i; } } return (maxIndex, max); } public static (TSource item, TMax max) MaxBy<TSource, TMax>(this IEnumerable<TSource> source, Func<TSource, TMax> maxBySelector) where TMax : IComparable<TMax> { TMax max; TSource maxByItem; var e = source.GetEnumerator(); e.MoveNext(); maxByItem = e.Current; max = maxBySelector(maxByItem); while (e.MoveNext()) { var item = e.Current; var next = maxBySelector(item); if (max.CompareTo(next) < 0) { max = next; maxByItem = item; } } return (maxByItem, max); } public static (int index, T min) MinBy<T>(this T[] arr) where T : IComparable<T> { T min = arr[0]; int minIndex = 0; for (int i = 0; i < arr.Length; i++) { if (min.CompareTo(arr[i]) > 0) { min = arr[i]; minIndex = i; } } return (minIndex, min); } public static (int index, T min) MinBy<T, TMin>(this T[] arr, Func<T, TMin> minBySelector) where TMin : IComparable<TMin> { var minItem = minBySelector(arr[0]); var min = arr[0]; int minIndex = 0; for (int i = 0; i < arr.Length; i++) { var nx = minBySelector(arr[i]); if (minItem.CompareTo(nx) > 0) { minItem = nx; min = arr[i]; minIndex = i; } } return (minIndex, min); } public static (TSource item, TMin min) MinBy<TSource, TMin>(this IEnumerable<TSource> source, Func<TSource, TMin> minBySelector) where TMin : IComparable<TMin> { TMin min; TSource minByItem; var e = source.GetEnumerator(); e.MoveNext(); minByItem = e.Current; min = minBySelector(minByItem); while (e.MoveNext()) { var item = e.Current; var next = minBySelector(item); if (min.CompareTo(next) > 0) { min = next; minByItem = item; } } return (minByItem, min); } public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count()); public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i); public static Span<T> AsSpan<T>(this List<T> list, int start = 0) => Unsafe.As<Tuple<T[]>>(list).Item1.AsSpan(start, list.Count); public static ref T Get<T>(this T[] arr, int index) { if (index < 0) return ref arr[arr.Length + index]; return ref arr[index]; } public static TValue Get<TKey, TValue>(this IDictionary<TKey, TValue> dic, TKey key) { dic.TryGetValue(key, out var v); return v; } } public static class ExComparer<T> { class ExpressionComparer<K> : IComparer<T> where K : IComparable<K> { private class ParameterReplaceVisitor : ExpressionVisitor { private readonly ParameterExpression from; private readonly ParameterExpression to; public ParameterReplaceVisitor(ParameterExpression from, ParameterExpression to) { this.from = from; this.to = to; } protected override Expression VisitParameter(ParameterExpression node) => node == from ? to : base.VisitParameter(node); } readonly Comparison<T> func; public ExpressionComparer(Expression<Func<T, K>> expression) { var paramA = expression.Parameters[0]; var paramB = Expression.Parameter(typeof(T)); var f2 = (Expression<Func<T, K>>)new ParameterReplaceVisitor(expression.Parameters[0], paramB).Visit(expression); var compExp = Expression.Lambda<Comparison<T>>(Expression.Call(expression.Body, typeof(K).GetMethod(nameof(IComparable<K>.CompareTo), new[] { typeof(K) }), f2.Body), paramA, paramB); this.func = compExp.Compile(); } public int Compare(T x, T y) => func(x, y); public override bool Equals(object obj) => obj is ExpressionComparer<K> c && this.func == c.func; public override int GetHashCode() => func.GetHashCode(); } class ReverseComparer : IComparer<T> { private static Comparer<T> orig = Comparer<T>.Default; public int Compare(T y, T x) => orig.Compare(x, y); public override bool Equals(object obj) => obj is ReverseComparer; public override int GetHashCode() => GetType().GetHashCode(); } public static IComparer<T> CreateExp<K>(Expression<Func<T, K>> expression) where K : IComparable<K> => new ExpressionComparer<K>(expression); public static readonly IComparer<T> DefaultReverse = new ReverseComparer(); } public class ΔDebugView<T> { private IEnumerable<T> collection; public ΔDebugView(IEnumerable<T> collection) { this.collection = collection ?? throw new ArgumentNullException(nameof(collection)); }[DebuggerBrowsable(DebuggerBrowsableState.RootHidden)] public T[] Items => collection.ToArray(); }[DebuggerStepThrough] public class ConsoleReader { const int BufSize = 1 << 12; private readonly byte[] buffer = new byte[BufSize]; private readonly Stream input; private readonly Encoding encoding; private int pos = 0; private int len = 0; public ConsoleReader(Stream input, Encoding encoding) { this.input = input; this.encoding = encoding; } public ConsoleReader() : this(Console.OpenStandardInput(), Console.InputEncoding) { }[MethodImpl(MethodImplOptions.AggressiveInlining)] private void MoveNext() { if (++pos >= len) { len = input.Read(buffer, 0, buffer.Length); if (len == 0) { buffer[0] = 10; } pos = 0; } } public int Int { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { int res = 0; bool neg = false; while (buffer[pos] < 48) { neg = buffer[pos] == 45; MoveNext(); } do { res = checked(res * 10 + (buffer[pos] ^ 48)); MoveNext(); } while (48 <= buffer[pos]); return neg ? -res : res; } } public int Int0 => this.Int - 1; public long Long { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { long res = 0; bool neg = false; while (buffer[pos] < 48) { neg = buffer[pos] == 45; MoveNext(); } do { res = res * 10 + (buffer[pos] ^ 48); MoveNext(); } while (48 <= buffer[pos]); return neg ? -res : res; } } public long Long0 => this.Long - 1; public string String { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { var sb = new List<byte>(); while (buffer[pos] <= 32) MoveNext(); do { sb.Add(buffer[pos]); MoveNext(); } while (32 < buffer[pos]); return this.encoding.GetString(sb.ToArray()); } } public string Ascii { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { var sb = new StringBuilder(); while (buffer[pos] <= 32) MoveNext(); do { sb.Append((char)buffer[pos]); MoveNext(); } while (32 < buffer[pos]); return sb.ToString(); } } public string Line { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { var sb = new List<byte>(); while (buffer[pos] <= 32) MoveNext(); do { sb.Add(buffer[pos]); MoveNext(); } while (buffer[pos] != 10 && buffer[pos] != 13); return this.encoding.GetString(sb.ToArray()); } } public char Char { [MethodImpl(MethodImplOptions.AggressiveInlining)] get { while (buffer[pos] <= 32) MoveNext(); char res = (char)buffer[pos]; MoveNext(); return res; } } public double Double => double.Parse(this.Ascii);[DebuggerStepThrough] public struct RepeatReader { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public T[] Select<T>(Func<ConsoleReader, T> factory) { var arr = new T[count]; for (var i = 0; i < count; i++) arr[i] = factory(cr); return arr; } public T[] Select<T>(Func<ConsoleReader, int, T> factory) { var arr = new T[count]; for (var i = 0; i < count; i++) arr[i] = factory(cr, i); return arr; } public string[] Line { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.Line; return arr; } } public string[] String { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.String; return arr; } } public string[] Ascii { get { var arr = new string[count]; for (var i = 0; i < count; i++) arr[i] = cr.Ascii; return arr; } } public int[] Int { get { var arr = new int[count]; for (var i = 0; i < count; i++) arr[i] = cr.Int; return arr; } } public int[] Int0 { get { var arr = new int[count]; for (var i = 0; i < count; i++) arr[i] = cr.Int0; return arr; } } public long[] Long { get { var arr = new long[count]; for (var i = 0; i < count; i++) arr[i] = cr.Long; return arr; } } public long[] Long0 { get { var arr = new long[count]; for (var i = 0; i < count; i++) arr[i] = cr.Long0; return arr; } } public double[] Double { get { var arr = new double[count]; for (var i = 0; i < count; i++) arr[i] = cr.Double; return arr; } } public static implicit operator int[](RepeatReader rr) => rr.Int; public static implicit operator long[](RepeatReader rr) => rr.Long; public static implicit operator double[](RepeatReader rr) => rr.Double; public static implicit operator string[](RepeatReader rr) => rr.Ascii; } public RepeatReader Repeat(int count) => new RepeatReader(this, count);[DebuggerStepThrough] public struct SplitReader { ConsoleReader cr; public SplitReader(ConsoleReader cr) { this.cr = cr; } public string[] String { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<string>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.String); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public string[] Ascii { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<string>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Ascii); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public int[] Int { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<int>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Int); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public int[] Int0 { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<int>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Int0); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public long[] Long { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<long>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Long); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public long[] Long0 { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<long>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Long0); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public double[] Double { get { while (cr.buffer[cr.pos] <= 32) cr.MoveNext(); var list = new List<double>(); do { if (cr.buffer[cr.pos] < 32) cr.MoveNext(); else list.Add(cr.Double); } while (cr.buffer[cr.pos] != 10 && cr.buffer[cr.pos] != 13); return list.ToArray(); } } public static implicit operator int[](SplitReader sr) => sr.Int; public static implicit operator long[](SplitReader sr) => sr.Long; public static implicit operator double[](SplitReader sr) => sr.Double; public static implicit operator string[](SplitReader sr) => sr.Ascii; } public SplitReader Split => new SplitReader(this); public static implicit operator int(ConsoleReader cr) => cr.Int; public static implicit operator long(ConsoleReader cr) => cr.Long; public static implicit operator double(ConsoleReader cr) => cr.Double; public static implicit operator string(ConsoleReader cr) => cr.Ascii; }[DebuggerStepThrough] public class ConsoleWriter {[DebuggerBrowsable(DebuggerBrowsableState.Never)] public readonly StreamWriter sw; public ConsoleWriter() : this(Console.OpenStandardOutput(), Console.OutputEncoding) { } public ConsoleWriter(Stream output, Encoding encoding) { sw = new StreamWriter(output, encoding); } public void Flush() => sw.Flush(); public ConsoleWriter WriteLine(ReadOnlySpan<char> obj) { sw.WriteLine(obj); return this; } public ConsoleWriter WriteLine<T>(T obj) { sw.WriteLine(obj.ToString()); return this; } public ConsoleWriter WriteLineJoin<T>(Span<T> col) => WriteMany(' ', (ReadOnlySpan<T>)col); public ConsoleWriter WriteLineJoin<T>(ReadOnlySpan<T> col) => WriteMany(' ', col); public ConsoleWriter WriteLineJoin<T>(IEnumerable<T> col) => WriteMany(' ', col); public ConsoleWriter WriteLineJoin<T>(params T[] col) => WriteMany(' ', col); public ConsoleWriter WriteLineJoin(params object[] col) => WriteMany(' ', col); public ConsoleWriter WriteLineJoin<T1, T2>(T1 v1, T2 v2) { sw.Write(v1.ToString()); sw.Write(' '); sw.WriteLine(v2.ToString()); return this; } public ConsoleWriter WriteLineJoin<T1, T2, T3>(T1 v1, T2 v2, T3 v3) { sw.Write(v1.ToString()); sw.Write(' '); sw.Write(v2.ToString()); sw.Write(' '); sw.WriteLine(v3.ToString()); return this; } public ConsoleWriter WriteLineJoin<T1, T2, T3, T4>(T1 v1, T2 v2, T3 v3, T4 v4) { sw.Write(v1.ToString()); sw.Write(' '); sw.Write(v2.ToString()); sw.Write(' '); sw.Write(v3.ToString()); sw.Write(' '); sw.WriteLine(v4.ToString()); return this; } public ConsoleWriter WriteLines<T>(Span<T> col) => WriteMany('\n', (ReadOnlySpan<T>)col); public ConsoleWriter WriteLines<T>(ReadOnlySpan<T> col) => WriteMany('\n', col); public ConsoleWriter WriteLines<T>(IEnumerable<T> col) => WriteMany('\n', col); public ConsoleWriter WriteLineGrid<T>(IEnumerable<IEnumerable<T>> cols) { foreach (var col in cols) WriteLineJoin(col); return this; } private ConsoleWriter WriteMany<T>(char sep, ReadOnlySpan<T> col) { var en = col.GetEnumerator(); if (!en.MoveNext()) return this; sw.Write(en.Current.ToString()); while (en.MoveNext()) { sw.Write(sep); sw.Write(en.Current.ToString()); } sw.WriteLine(); return this; } private ConsoleWriter WriteMany<T>(char sep, IEnumerable<T> col) { var en = col.GetEnumerator(); if (!en.MoveNext()) return this; sw.Write(en.Current.ToString()); while (en.MoveNext()) { sw.Write(sep); sw.Write(en.Current.ToString()); } sw.WriteLine(); return this; } } }
public partial class Program {[System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] public ConsoleReader cr;[System.Diagnostics.DebuggerBrowsable(System.Diagnostics.DebuggerBrowsableState.Never)] public ConsoleWriter cw; public Program(ConsoleReader reader, ConsoleWriter writer) { this.cr = reader; this.cw = writer; System.Globalization.CultureInfo.CurrentCulture = System.Globalization.CultureInfo.InvariantCulture; } static void Main() => new Program(new ConsoleReader(), new ConsoleWriter()).Run(); public void Run() { var res = Calc(); if (res is double) cw.WriteLine(Result((double)res)); else if (res is bool) cw.WriteLine(Result((bool)res)); else if (res != null) cw.WriteLine(res.ToString()); cw.Flush(); } }
public partial class Program
{
    public static string Result(double d) => d.ToString("0.####################", System.Globalization.CultureInfo.InvariantCulture);
    #endregion
    public static string Result(bool b) => b ? "Yes" : "No";
    private object Calc()
    {
        N = cr;
        M = cr;
        long[] arr = cr.Repeat(N);
        long[] brr = cr.Repeat(M);
        cw.WriteLineJoin(new Convolution(998244353).畳み込み(arr, brr));
        return null;
    }
    int N,M;
}



class Convolution { public readonly int mod; public Convolution(int mod) { this.mod = mod; (sum_e, sum_ie) = BuildSum(); } long[] sum_e; long[] sum_ie; static Dictionary<int, int> primitiveRootCache = new Dictionary<int, int> { { 2, 1 }, { 167772161, 3 }, { 469762049, 3 }, { 754974721, 11 }, { 998244353, 3 }, }; static int PrimitiveRoot(int p) { if (primitiveRootCache.TryGetValue(p, out var val)) return val; Span<int> divs = stackalloc int[20]; divs[0] = 2; int cnt = 1; int x = (p - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long)i * i <= x; i += 2) if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) x /= i; } if (x > 1) divs[cnt++] = x; for (int g = 2; ; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (PowMod(g, (p - 1) / divs[i], p) == 1) { ok = false; break; } } if (ok) return primitiveRootCache[p] = g; } } static long PowMod(long x, int n, int mod) { if (mod == 1) return 0; long r = 1; long y = x % mod; if (y < 0) y += mod; while (n > 0) { if ((n & 1) != 0) r = r * y % mod; y = y * y % mod; n >>= 1; } return r; } static long Inverse(long a, int mod) { long b = mod, u = 1, v = 0; while (b > 0) { long t = a / b; (a, b) = (b, a - t * b); (u, v) = (v, u - t * v); } u %= mod; if (u < 0) u += mod; return u; } (long[] sum_e, long[] sum_ie) BuildSum() { var g = PrimitiveRoot(mod); var sum_e = new long[30]; var sum_ie = new long[30]; Span<long> es = stackalloc long[30]; Span<long> ies = stackalloc long[30]; int cnt2 = LSB(mod - 1); long e = PowMod(g, (mod - 1) >> cnt2, mod); long ie = Inverse(e, mod); for (int i = cnt2; i >= 2; i--) { es[i - 2] = e; ies[i - 2] = ie; e = e * e % mod; ie = ie * ie % mod; } long now = 1; long inow = 1; for (int i = 0; i < cnt2 - 2; i++) { sum_e[i] = es[i] * now % mod; sum_ie[i] = ies[i] * inow % mod; now = now * ies[i] % mod; inow = inow * es[i] % mod; } return (sum_e, sum_ie); } void Butterfly(long[] a) { int h = MSB(a.Length - 1) + 1; for (int ph = 1; ph <= h; ph++) { int w = 1 << (ph - 1), p = 1 << (h - ph); long now = 1; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { long l = a[i + offset]; long r = a[i + offset + p] * now % mod; a[i + offset] = l + r; if (a[i + offset] >= mod) a[i + offset] -= mod; a[i + offset + p] = l - r; if (a[i + offset + p] < 0) a[i + offset + p] += mod; } now = now * sum_e[LSB(~(uint)s)] % mod; } } } void ButterflyInv(long[] a) { int h = MSB(a.Length - 1) + 1; for (int ph = h; ph >= 1; ph--) { int w = 1 << (ph - 1), p = 1 << (h - ph); long inow = 1; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { long l = a[i + offset]; long r = a[i + offset + p]; a[i + offset] = l + r; if (a[i + offset] >= mod) a[i + offset] -= mod; a[i + offset + p] = l - r; if (a[i + offset + p] < 0) a[i + offset + p] += mod; a[i + offset + p] = a[i + offset + p] * inow % mod; } inow = inow * sum_ie[LSB(~(uint)s)] % mod; } } } public long[] 畳み込み(long[] arr, long[] brr) { if (arr.Length == 0 || brr.Length == 0) return Array.Empty<long>(); if (Math.Min(arr.Length, brr.Length) <= 60) return Small(arr, brr, mod); var z = 1 << (MSB(arr.Length + brr.Length - 1 - 1) + 1); var arrz = new long[z]; var brrz = new long[z]; for (int i = 0; i < arr.Length; i++) arrz[i] = arr[i] % mod; for (int i = 0; i < brr.Length; i++) brrz[i] = brr[i] % mod; Butterfly(arrz); Butterfly(brrz); for (int i = 0; i < arrz.Length; i++) arrz[i] = arrz[i] * brrz[i] % mod; ButterflyInv(arrz); var res = new long[arr.Length + brr.Length - 1]; var iz = Inverse(z, mod); for (int i = 0; i < res.Length; i++) { res[i] = arrz[i] * iz % mod; } return res; static long[] Small(long[] arr, long[] brr, long mod) { if (arr.Length < brr.Length) (arr, brr) = (brr, arr); var res = new long[arr.Length + brr.Length - 1]; for (int i = 0; i < arr.Length; i++) for (int j = 0; j < brr.Length; j++) { res[i + j] += arr[i] * brr[j] % mod; if (res[i + j] >= mod) res[i + j] -= mod; } return res; } } public static long[] 畳み込みLong(long[] arr, long[] brr) { if (arr.Length == 0 || brr.Length == 0) return Array.Empty<long>(); const ulong MOD1 = 754974721; const ulong MOD2 = 167772161; const ulong MOD3 = 469762049; const ulong M2M3 = MOD2 * MOD3; const ulong M1M3 = MOD1 * MOD3; const ulong M1M2 = MOD1 * MOD2; const ulong M1M2M3 = unchecked(MOD1 * MOD2 * MOD3); const ulong i1 = 190329765; const ulong i2 = 58587104; const ulong i3 = 187290749; var c1 = new Convolution((int)MOD1).畳み込み(arr, brr); var c2 = new Convolution((int)MOD2).畳み込み(arr, brr); var c3 = new Convolution((int)MOD3).畳み込み(arr, brr); ReadOnlySpan<ulong> offset = stackalloc ulong[5] { 0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3 }; var res = new long[arr.Length + brr.Length - 1]; for (int i = 0; i < res.Length; i++) { ulong x = 0; x += ((ulong)c1[i] * i1) % MOD1 * M2M3; x += ((ulong)c2[i] * i2) % MOD2 * M1M3; x += ((ulong)c3[i] * i3) % MOD3 * M1M2; var mm = ((long)x) % (long)MOD1; if (mm < 0) mm += (long)MOD1; long diff = c1[i] - mm; if (diff < 0) diff += (long)MOD1; x -= offset[(int)(diff % 5)]; res[i] = (long)x; } return res; } }