結果
| 問題 |
No.2413 Multiple of 99
|
| コンテスト | |
| ユーザー |
 KumaTachiRen
|
| 提出日時 | 2023-09-29 09:04:00 |
| 言語 | C# (.NET 8.0.404) |
| 結果 |
AC
|
| 実行時間 | 2,958 ms / 8,000 ms |
| コード長 | 37,412 bytes |
| コンパイル時間 | 15,002 ms |
| コンパイル使用メモリ | 167,596 KB |
| 実行使用メモリ | 199,796 KB |
| 最終ジャッジ日時 | 2024-07-22 03:41:38 |
| 合計ジャッジ時間 | 49,991 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 21 |
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 (95 ms)。 MSBuild のバージョン 17.9.6+a4ecab324 (.NET) 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;
using System.ComponentModel;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Diagnostics.Contracts;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.Intrinsics.X86;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Text;
using static Functions;
using static OutputLib;
using ModInt = StaticModInt<Mod998244353>;
static class Program
{
static public void Main(string[] args)
{
Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
new Solver();
Console.Out.Flush();
}
}
public class Solver
{
public Solver()
{
Solve();
}
void Solve()
{
int n = ri, k = ri;
var f = new ModInt[10];
var g = new ModInt[10];
for (int i = 0; i < 10; i++)
{
f[i] = 1;
g[i] = 1;
}
f = Pow(f, (n + 1) / 2);
g = Pow(g, n / 2);
var h = new ModInt[f.Length + g.Length - 1];
for (int j = 0; j < 11; j++)
{
var u = new ModInt[f.Length];
var v = new ModInt[g.Length];
for (int i = j; i < f.Length; i += 11)
u[i] = f[i];
for (int i = j; i < g.Length; i += 11)
v[i] = g[i];
var w = MathLib.Convolution(u, v);
for (int i = 0; i < w.Length; i++)
h[i] += w[i];
}
ModInt ans = 0;
for (int i = 0; i < h.Length; i += 9) ans += h[i] * ((ModInt)i).Pow(k);
Write(ans);
}
ModInt[] Pow(ModInt[] f, int n)
{
var r = new ModInt[1] { 1 };
while (n > 0)
{
if (n % 2 == 1) r = MathLib.Convolution(r, f);
f = MathLib.Convolution(f, f);
n /= 2;
}
return r;
}
const long INF = 1L << 60;
int ri { [MethodImpl(256)] get => (int)sc.Integer(); }
(int, int) ri2 { [MethodImpl(256)] get => (ri, ri); }
(int, int, int) ri3 { [MethodImpl(256)] get => (ri, ri, ri); }
(int, int, int, int) ri4 { [MethodImpl(256)] get => (ri, ri, ri, ri); }
(int, int, int, int, int) ri5 { [MethodImpl(256)] get => (ri, ri, ri, ri, ri); }
long rl { [MethodImpl(256)] get => sc.Integer(); }
(long, long) rl2 { [MethodImpl(256)] get => (rl, rl); }
(long, long, long) rl3 { [MethodImpl(256)] get => (rl, rl, rl); }
(long, long, long, long) rl4 { [MethodImpl(256)] get => (rl, rl, rl, rl); }
(long, long, long, long, long) rl5 { [MethodImpl(256)] get => (rl, rl, rl, rl, rl); }
uint rui { [MethodImpl(256)] get => (uint)sc.UInteger(); }
ulong rul { [MethodImpl(256)] get => sc.UInteger(); }
double rd { [MethodImpl(256)] get => sc.Double(); }
string rs { [MethodImpl(256)] get => sc.Scan(); }
string rline { [MethodImpl(256)] get => sc.Line(); }
public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
}
public static class Functions
{
[MethodImpl(256)]
public static int Popcount(ulong x)
{
x = (x & 0x5555555555555555UL) + ((x >> 1) & 0x5555555555555555UL);
x = (x & 0x3333333333333333UL) + ((x >> 2) & 0x3333333333333333UL);
x = (x & 0x0f0f0f0f0f0f0f0fUL) + ((x >> 4) & 0x0f0f0f0f0f0f0f0fUL);
x = (x & 0x00ff00ff00ff00ffUL) + ((x >> 8) & 0x00ff00ff00ff00ffUL);
x = (x & 0x0000ffff0000ffffUL) + ((x >> 16) & 0x0000ffff0000ffffUL);
x = (x & 0x00000000ffffffffUL) + ((x >> 32) & 0x00000000ffffffffUL);
return (int)x;
}
[MethodImpl(256)]
public static int Popcount(int x)
{
x = (x & 0x55555555) + ((x >> 1) & 0x55555555);
x = (x & 0x33333333) + ((x >> 2) & 0x33333333);
x = (x & 0x0f0f0f0f) + ((x >> 4) & 0x0f0f0f0f);
x = (x & 0x00ff00ff) + ((x >> 8) & 0x00ff00ff);
x = (x & 0x0000ffff) + ((x >> 16) & 0x0000ffff);
return x;
}
[MethodImpl(256)]
public static int Ctz(long x)
{
if (x == 0) return -1;
return Popcount((ulong)((x & -x) - 1));
}
[MethodImpl(256)]
public static int CeilPow2(int n)
{
int x = 0;
while ((1 << x) < n) x++;
return x;
}
[MethodImpl(256)]
public static int SafeMod(int x, int m)
{
int r = x % m;
return r < 0 ? r + Math.Abs(m) : r;
}
[MethodImpl(256)]
public static long SafeMod(long x, long m)
{
long r = x % m;
return r < 0 ? r + Math.Abs(m) : r;
}
[MethodImpl(256)] public static int Sign(long x) => x == 0 ? 0 : (x < 0 ? -1 : 1);
[MethodImpl(256)] public static int Sign(double x) => x == 0 ? 0 : (x < 0 ? -1 : 1);
[MethodImpl(256)] public static int DigitSum(long n, int d = 10) { long s = 0; while (n > 0) { s += n % d; n /= d; } return (int)s; }
[MethodImpl(256)] public static long Floor(long a, long b) => a >= 0 ? a / b : (a + 1) / b - 1;
[MethodImpl(256)] public static long Ceil(long a, long b) => a > 0 ? (a - 1) / b + 1 : a / b;
[MethodImpl(256)] public static int Gcd(int a, int b) => b == 0 ? a : Gcd(b, a % b);
[MethodImpl(256)] public static long Gcd(long a, long b) => b == 0 ? a : Gcd(b, a % b);
[MethodImpl(256)] public static (long x, long y, long g) ExtGcd(long a, long b) { if (b == 0) return (Sign(a), 0, Math.Abs(a)); long c = SafeMod(a, b); var (x2, y2, g) = ExtGcd(b, c); long x = SafeMod(y2, b); long y = (g - a * x) / b; return (x, y, g); }
[MethodImpl(256)] public static void Swap(ref int x, ref int y) { x ^= y; y ^= x; x ^= y; }
[MethodImpl(256)] public static void Swap(ref long x, ref long y) { x ^= y; y ^= x; x ^= y; }
[MethodImpl(256)] public static void Swap<T>(ref T x, ref T y) { T t = y; y = x; x = t; }
[MethodImpl(256)] public static T Clamp<T>(T x, T l, T r) where T : IComparable<T> => x.CompareTo(l) <= 0 ? l : (x.CompareTo(r) <= 0 ? x : r);
[MethodImpl(256)] public static T Clamp<T>(ref T x, T l, T r) where T : IComparable<T> => x = x.CompareTo(l) <= 0 ? l : (x.CompareTo(r) <= 0 ? x : r);
[MethodImpl(256)] public static void Chmin<T>(ref T x, T y) where T : IComparable<T> { if (x.CompareTo(y) > 0) x = y; }
[MethodImpl(256)] public static void Chmax<T>(ref T x, T y) where T : IComparable<T> { if (x.CompareTo(y) < 0) x = y; }
[MethodImpl(256)] public static int LowerBound(long[] arr, long val, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), t => Sign(t - val), l, r);
[MethodImpl(256)] public static int LowerBound(int[] arr, int val, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), t => t - val, l, r);
[MethodImpl(256)] public static int LowerBound<T>(T[] arr, T val, int l = -1, int r = -1) where T : IComparable<T> => LowerBound(arr.AsSpan(), t => t.CompareTo(val), l, r);
[MethodImpl(256)] public static int LowerBound<T>(T[] arr, Func<T, int> comp, int l = -1, int r = -1) => LowerBound(arr.AsSpan(), comp, l, r);
[MethodImpl(256)] public static int LowerBound<T>(Span<T> data, Func<T, int> comp, int l = -1, int r = -1) { if (data.Length == 0) return -1; if (l == -1) l = 0; if (r == -1) r = data.Length; while (l < r) { int x = (l + r) / 2; if (comp(data[x]) < 0) l = x + 1; else r = x; } return l; }
[MethodImpl(256)] public static string ToBase2(long v, int digit = -1) { if (digit == -1) { digit = 0; while ((v >> digit) > 0) digit++; } var c = new string[digit]; for (int i = 0; i < digit; i++) c[digit - 1 - i] = ((v >> i) & 1) == 0 ? "0" : "1"; return string.Join("", c); }
[MethodImpl(256)] public static string ToBaseN(long v, int n, int digit = -1) { if (digit == -1) { digit = 0; long pow = 1; while (v >= pow) { digit++; pow *= n; } } var c = new int[digit]; for (int i = 0; i < digit; i++, v /= n) c[digit - 1 - i] = (int)(v % n); return string.Join("", c); }
}
public class StreamScanner
{
public StreamScanner(Stream stream) { str = stream; }
private readonly Stream str;
private readonly byte[] buf = new byte[1024];
private int len, ptr;
public bool isEof = false;
public bool IsEndOfStream { get { return isEof; } }
[MethodImpl(256)] private byte read() { if (isEof) throw new EndOfStreamException(); if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; }
[MethodImpl(256)] public char Char() { byte b = 0; do b = read(); while (b < 33 || 126 < b); return (char)b; }
[MethodImpl(256)] public string Line() { var sb = new StringBuilder(); for (var b = Char(); b != 10 && !isEof; b = (char)read()) sb.Append(b); return sb.ToString(); }
[MethodImpl(256)] public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); }
[MethodImpl(256)] public long Integer() { long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != '-' && (b < '0' || '9' < b)); if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } }
[MethodImpl(256)] public ulong UInteger() { ulong ret = 0; byte b = 0; do b = read(); while (b < '0' || '9' < b); for (; true; b = read()) { if (b < '0' || '9' < b) return ret; else ret = ret * 10 + b - '0'; } }
[MethodImpl(256)] public double Double() => double.Parse(Scan());
}
public static class OutputLib
{
[MethodImpl(256)] public static void WriteJoin<T>(string s, IEnumerable<T> t) => Console.WriteLine(string.Join(s, t));
[MethodImpl(256)] public static void WriteMat<T>(T[,] a) { int sz1 = a.GetLength(0); int sz2 = a.GetLength(1); for (int i = 0; i < sz1; i++) { var b = new T[sz2]; for (int j = 0; j < sz2; j++) b[j] = a[i, j]; WriteJoin(" ", b); } }
[MethodImpl(256)] public static void WriteMat<T>(T[][] a) { for (int i = 0; i < a.Length; i++) WriteJoin(" ", a[i]); }
[MethodImpl(256)] public static void Write(object t) => Console.WriteLine(t.ToString());
[MethodImpl(256)] public static void Write(string str) => Console.WriteLine(str);
[MethodImpl(256)] public static void Write(string str, object arg1) => Console.WriteLine(str, arg1);
[MethodImpl(256)] public static void Write(string str, object arg1, object arg2) => Console.WriteLine(str, arg1, arg2);
[MethodImpl(256)] public static void Write(string str, object arg1, object arg2, object arg3) => Console.WriteLine(str, arg1, arg2, arg3);
[MethodImpl(256)] public static void Write(string str, params object[] arg) => Console.WriteLine(str, arg);
[MethodImpl(256)] public static void WriteFlush(object t) { Console.WriteLine(t.ToString()); Console.Out.Flush(); }
[MethodImpl(256)] public static void WriteError(object t) => Console.Error.WriteLine(t.ToString());
[MethodImpl(256)] public static void Flush() => Console.Out.Flush();
[MethodImpl(256)] public static void YN(bool t) => Console.WriteLine(t ? "YES" : "NO");
[MethodImpl(256)] public static void Yn(bool t) => Console.WriteLine(t ? "Yes" : "No");
[MethodImpl(256)] public static void yn(bool t) => Console.WriteLine(t ? "yes" : "no");
}
public interface IStaticMod
{
uint Mod { get; }
bool IsPrime { get; }
}
public readonly struct Mod1000000007 : IStaticMod
{
public uint Mod => 1000000007;
public bool IsPrime => true;
}
public readonly struct Mod998244353 : IStaticMod
{
public uint Mod => 998244353;
public bool IsPrime => true;
}
public readonly struct StaticModInt<T> : IEquatable<StaticModInt<T>>, IFormattable where T : struct, IStaticMod
{
internal readonly uint _v;
private static readonly T op = default;
public int Value => (int)_v;
public static int Mod => (int)op.Mod;
public static StaticModInt<T> Zero => default;
public static StaticModInt<T> One => new StaticModInt<T>(1u);
[MethodImpl(256)]
public static StaticModInt<T> Raw(int v)
{
var u = unchecked((uint)v);
return new StaticModInt<T>(u);
}
[MethodImpl(256)]
public StaticModInt(long v) : this(Round(v)) { }
[MethodImpl(256)]
public StaticModInt(ulong v) : this((uint)(v % op.Mod)) { }
[MethodImpl(256)]
private StaticModInt(uint v) => _v = v;
[MethodImpl(256)]
private static uint Round(long v)
{
var x = v % op.Mod;
if (x < 0) x += op.Mod;
return (uint)x;
}
[MethodImpl(256)]
public static StaticModInt<T> operator ++(StaticModInt<T> v)
{
var x = v._v + 1;
if (x == op.Mod) x = 0;
return new StaticModInt<T>(x);
}
[MethodImpl(256)]
public static StaticModInt<T> operator --(StaticModInt<T> v)
{
var x = v._v;
if (x == 0) x = op.Mod;
return new StaticModInt<T>(x - 1);
}
[MethodImpl(256)]
public static StaticModInt<T> operator +(StaticModInt<T> lhs, StaticModInt<T> rhs)
{
var v = lhs._v + rhs._v;
if (v >= op.Mod) v -= op.Mod;
return new StaticModInt<T>(v);
}
[MethodImpl(256)]
public static StaticModInt<T> operator -(StaticModInt<T> lhs, StaticModInt<T> rhs)
{
unchecked
{
var v = lhs._v - rhs._v;
if (v >= op.Mod) v += op.Mod;
return new StaticModInt<T>(v);
}
}
[MethodImpl(256)]
public static StaticModInt<T> operator *(StaticModInt<T> lhs, StaticModInt<T> rhs) => new StaticModInt<T>((uint)((ulong)lhs._v * rhs._v % op.Mod));
[MethodImpl(256)]
public static StaticModInt<T> operator /(StaticModInt<T> lhs, StaticModInt<T> rhs) => lhs * rhs.Inv();
[MethodImpl(256)]
public static StaticModInt<T> operator +(StaticModInt<T> v) => v;
[MethodImpl(256)]
public static StaticModInt<T> operator -(StaticModInt<T> v) => new StaticModInt<T>(v._v == 0 ? 0 : op.Mod - v._v);
[MethodImpl(256)]
public static bool operator ==(StaticModInt<T> lhs, StaticModInt<T> rhs) => lhs._v == rhs._v;
[MethodImpl(256)]
public static bool operator !=(StaticModInt<T> lhs, StaticModInt<T> rhs) => lhs._v != rhs._v;
[MethodImpl(256)]
public static implicit operator StaticModInt<T>(int v) => new StaticModInt<T>(v);
[MethodImpl(256)]
public static implicit operator StaticModInt<T>(uint v) => new StaticModInt<T>((long)v);
[MethodImpl(256)]
public static implicit operator StaticModInt<T>(long v) => new StaticModInt<T>(v);
[MethodImpl(256)]
public static implicit operator StaticModInt<T>(ulong v) => new StaticModInt<T>(v);
[MethodImpl(256)]
public static implicit operator long(StaticModInt<T> v) => v._v;
[MethodImpl(256)]
public static implicit operator ulong(StaticModInt<T> v) => v._v;
[MethodImpl(256)]
public StaticModInt<T> Pow(long n)
{
var x = this;
var r = new StaticModInt<T>(1U);
while (n > 0)
{
if ((n & 1) > 0) r *= x;
x *= x;
n >>= 1;
}
return r;
}
[MethodImpl(256)]
public StaticModInt<T> Inv()
{
var (x, y, g) = ExtGcd(_v, op.Mod);
return new StaticModInt<T>(x);
}
[MethodImpl(256)]
static (long x, long y, long g) ExtGcd(long a, long b)
{
if (b == 0) return a >= 0 ? (1, 0, a) : (-1, 0, -a);
long c = SafeMod(a, b);
var (x2, y2, g) = ExtGcd(b, c);
long x = SafeMod(y2, b);
long y = (g - a * x) / b;
return (x, y, g);
}
[MethodImpl(256)]
static long SafeMod(long x, long m)
{
long r = x % m;
if (r < 0) r += m;
return r;
}
[MethodImpl(256)]
public override string ToString() => _v.ToString();
[MethodImpl(256)]
public string ToString(string format, IFormatProvider formatProvider) => _v.ToString(format, formatProvider);
[MethodImpl(256)]
public override bool Equals(object obj) => obj is StaticModInt<T> m && Equals(m);
[MethodImpl(256)]
public bool Equals(StaticModInt<T> other) => _v == other._v;
[MethodImpl(256)]
public override int GetHashCode() => _v.GetHashCode();
}
public static partial class MathLib
{
[MethodImpl(256)]
public static long[] Convolution<TMod>(ReadOnlySpan<long> a, ReadOnlySpan<long> b) where TMod : struct, IStaticMod
{
var u = new StaticModInt<TMod>[a.Length];
for (int i = 0; i < a.Length; i++) u[i] = a[i];
var v = new StaticModInt<TMod>[b.Length];
for (int i = 0; i < b.Length; i++) v[i] = b[i];
u = Convolution(u, v);
var r = new long[u.Length];
for (int i = 0; i < u.Length; i++) r[i] = u[i];
return r;
}
[MethodImpl(256)]
public static StaticModInt<TMod>[] Convolution<TMod>(ReadOnlySpan<StaticModInt<TMod>> a, ReadOnlySpan<StaticModInt<TMod>> b) where TMod : struct, IStaticMod
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 0)
return Array.Empty<StaticModInt<TMod>>();
if (Math.Min(n, m) <= 30)
return ConvolutionNaive(a, b);
return ConvolutionFFT(a, b);
}
[MethodImpl(256)]
public static StaticModInt<TMod>[] Convolution<TMod>(StaticModInt<TMod>[] a, StaticModInt<TMod>[] b) where TMod : struct, IStaticMod
=> Convolution((ReadOnlySpan<StaticModInt<TMod>>)a, b);
[MethodImpl(256)]
private static StaticModInt<TMod>[] ConvolutionFFT<TMod>(ReadOnlySpan<StaticModInt<TMod>> a, ReadOnlySpan<StaticModInt<TMod>> b) where TMod : struct, IStaticMod
{
int n = a.Length, m = b.Length;
int z = 1 << InternalBit.CeilPow2(n + m - 1);
var a2 = new StaticModInt<TMod>[z];
var b2 = new StaticModInt<TMod>[z];
a.CopyTo(a2);
b.CopyTo(b2);
var result = ConvolutionFFTInner(a2, b2);
Array.Resize(ref result, n + m - 1);
var iz = new StaticModInt<TMod>(z).Inv();
for (int i = 0; i < result.Length; i++)
result[i] *= iz;
return result;
}
[MethodImpl(256)]
private static StaticModInt<TMod>[] ConvolutionFFTInner<TMod>(StaticModInt<TMod>[] a, StaticModInt<TMod>[] b) where TMod : struct, IStaticMod
{
Butterfly<TMod>.Calculate(a);
Butterfly<TMod>.Calculate(b);
for (int i = 0; i < a.Length; i++)
a[i] *= b[i];
Butterfly<TMod>.CalculateInv(a);
return a;
}
[MethodImpl(256)]
private static StaticModInt<TMod>[] ConvolutionNaive<TMod>(ReadOnlySpan<StaticModInt<TMod>> a, ReadOnlySpan<StaticModInt<TMod>> b) where TMod : struct, IStaticMod
{
if (a.Length < b.Length)
{
#pragma warning disable IDE0180
var temp = a;
a = b;
b = temp;
#pragma warning restore IDE0180
}
var ans = new StaticModInt<TMod>[a.Length + b.Length - 1];
for (int i = 0; i < a.Length; i++)
{
for (int j = 0; j < b.Length; j++)
{
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
[MethodImpl(256)]
public static long[] ConvolutionLong(ReadOnlySpan<long> a, ReadOnlySpan<long> b)
{
unchecked
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 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 = Mod1 * Mod2 * Mod3;
const ulong i1 = 190329765;
const ulong i2 = 58587104;
const ulong i3 = 187290749;
Debug.Assert(default(FFTMod1).Mod == Mod1);
Debug.Assert(default(FFTMod2).Mod == Mod2);
Debug.Assert(default(FFTMod3).Mod == Mod3);
Debug.Assert(i1 == (ulong)InternalMath.InvGcd((long)M2M3, (long)Mod1).Item2);
Debug.Assert(i2 == (ulong)InternalMath.InvGcd((long)M1M3, (long)Mod2).Item2);
Debug.Assert(i3 == (ulong)InternalMath.InvGcd((long)M1M2, (long)Mod3).Item2);
var c1 = Convolution<FFTMod1>(a, b);
var c2 = Convolution<FFTMod2>(a, b);
var c3 = Convolution<FFTMod3>(a, b);
var c = new long[n + m - 1];
for (int i = 0; i < c.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;
long diff = c1[i] - InternalMath.SafeMod((long)x, (long)Mod1);
if (diff < 0) diff += (long)Mod1;
switch (diff % 5)
{
case 2:
x -= M1M2M3;
break;
case 3:
x -= 2 * M1M2M3;
break;
case 4:
x -= 3 * M1M2M3;
break;
}
c[i] = (long)x;
}
return c;
}
}
[MethodImpl(256)]
public static StaticModInt<Mod>[] ConvolutionIntMod<Mod>(ReadOnlySpan<StaticModInt<Mod>> a, ReadOnlySpan<StaticModInt<Mod>> b) where Mod : struct, IStaticMod
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 0) return Array.Empty<StaticModInt<Mod>>();
const long Mod1 = 754974721;
const long Mod2 = 167772161;
const long Mod3 = 469762049;
const long M1invM2 = 95869806;
const long M12invM3 = 187290749;
int mod = StaticModInt<Mod>.Mod;
long M12mod = Mod1 * Mod2 % mod;
var u = new long[n];
for (int i = 0; i < n; i++) u[i] = a[i];
var v = new long[m];
for (int i = 0; i < m; i++) v[i] = b[i];
var c1 = Convolution<FFTMod1>(u, v);
var c2 = Convolution<FFTMod2>(u, v);
var c3 = Convolution<FFTMod3>(u, v);
var c = new StaticModInt<Mod>[n + m - 1];
for (int i = 0; i < c.Length; i++)
{
long v1 = (c2[i] - c1[i]) * M1invM2 % Mod2;
if (v1 < 0) v1 += Mod2;
long v2 = (c3[i] - (c1[i] + Mod1 * v1) % Mod3) * M12invM3 % Mod3;
if (v2 < 0) v2 += Mod3;
long v3 = (c1[i] + Mod1 * v1 + M12mod * v2) % mod;
if (v3 < 0) v3 += mod;
c[i] = v3;
}
return c;
}
private readonly struct FFTMod1 : IStaticMod
{
public uint Mod => 754974721;
public bool IsPrime => true;
}
private readonly struct FFTMod2 : IStaticMod
{
public uint Mod => 167772161;
public bool IsPrime => true;
}
private readonly struct FFTMod3 : IStaticMod
{
public uint Mod => 469762049;
public bool IsPrime => true;
}
}
public static class InternalBit
{
[MethodImpl(256)]
public static uint ExtractLowestSetBit(int n)
{
#if NETCOREAPP3_0_OR_GREATER
if (Bmi1.IsSupported)
{
return Bmi1.ExtractLowestSetBit((uint)n);
}
#endif
return (uint)(n & -n);
}
[MethodImpl(256)]
public static int Bsf(uint n)
{
#if EMBEDDING
Contract.Assert(n > 0, reason: $"{nameof(n)} must positive");
#endif
return BitOperations.TrailingZeroCount(n);
}
[MethodImpl(256)]
public static int CeilPow2(int n)
{
var un = (uint)n;
if (un <= 1) return 0;
return BitOperations.Log2(un - 1) + 1;
}
}
public static class InternalMath
{
private static readonly Dictionary<uint, int> primitiveRootsCache = new Dictionary<uint, int>()
{
{ 2, 1 },
{ 167772161, 3 },
{ 469762049, 3 },
{ 754974721, 11 },
{ 998244353, 3 }
};
[MethodImpl(256)]
public static int PrimitiveRoot<TMod>() where TMod : struct, IStaticMod
{
uint m = default(TMod).Mod;
Contract.Assert(m >= 2, $"{nameof(m)} must be greater or equal 2");
Contract.Assert(default(TMod).IsPrime, $"{nameof(m)} must be prime number");
#if NET7_0_OR_GREATER
ref var result = ref System.Runtime.InteropServices.CollectionsMarshal.GetValueRefOrAddDefault(primitiveRootsCache, m, out var exists);
if (!exists)
{
result = PrimitiveRootCalculate<TMod>();
}
return result;
#else
if (primitiveRootsCache.TryGetValue(m, out var p))
{
return p;
}
return primitiveRootsCache[m] = PrimitiveRootCalculate<TMod>();
#endif
}
static int PrimitiveRootCalculate<TMod>() where TMod : struct, IStaticMod
{
var m = default(TMod).Mod;
Span<uint> divs = stackalloc uint[20];
divs[0] = 2;
int cnt = 1;
var x = m - 1;
x >>= BitOperations.TrailingZeroCount(x);
for (uint i = 3; (long)i * i <= x; i += 2)
{
if (x % i == 0)
{
divs[cnt++] = i;
do
{
x /= i;
} while (x % i == 0);
}
}
if (x > 1)
{
divs[cnt++] = x;
}
divs = divs.Slice(0, cnt);
for (int g = 2; ; g++)
{
foreach (var d in divs)
if (new StaticModInt<TMod>(g).Pow((m - 1) / d).Value == 1)
goto NEXT;
return g;
NEXT:;
}
}
[MethodImpl(256)]
public static (long, long) InvGcd(long a, long b)
{
a = SafeMod(a, b);
if (a == 0) return (b, 0);
long s = b, t = a;
long m0 = 0, m1 = 1;
long u;
while (true)
{
if (t == 0)
{
if (m0 < 0) m0 += b / s;
return (s, m0);
}
u = s / t;
s -= t * u;
m0 -= m1 * u;
if (s == 0)
{
if (m1 < 0) m1 += b / t;
return (t, m1);
}
u = t / s;
t -= s * u;
m1 -= m0 * u;
}
}
[MethodImpl(256)]
public static long SafeMod(long x, long m)
{
x %= m;
if (x < 0) x += m;
return x;
}
[MethodImpl(256)]
public static bool IsPrime(int n)
{
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long d = n - 1;
while (d % 2 == 0) d /= 2;
ReadOnlySpan<byte> bases = stackalloc byte[3] { 2, 7, 61 };
foreach (long a in bases)
{
long t = d;
long y = PowMod(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1)
{
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0)
{
return false;
}
}
return true;
}
[MethodImpl(256)]
public static uint PowMod(long x, long n, int m)
{
Contract.Assert(0 <= n && 1 <= m, $"0 <= {nameof(n)} && 1 <= {nameof(m)}");
if (m == 1) return 0;
return new Barrett((uint)m).Pow(x, n);
}
[MethodImpl(256)]
public static uint PowMod(long x, long n, uint m)
{
Contract.Assert(0 <= n && 1 <= m, $"0 <= {nameof(n)} && 1 <= {nameof(m)}");
if (m == 1) return 0;
return new Barrett(m).Pow(x, n);
}
[MethodImpl(256)]
public static ulong FloorSumUnsigned(ulong n, ulong m, ulong a, ulong b)
{
ulong ans = 0;
while (true)
{
if (a >= m)
{
ans += (n - 1) * n / 2 * (a / m);
a %= m;
}
if (b >= m)
{
ans += n * (b / m);
b %= m;
}
ulong yMax = a * n + b;
if (yMax < m) return ans;
(n, m, a, b) = (yMax / m, a, m, yMax % m);
}
}
[MethodImpl(256)]
public static ulong Mul128Bit(ulong a, ulong b)
{
#if NETCOREAPP3_1_OR_GREATER
if (Bmi2.X64.IsSupported)
return Bmi2.X64.MultiplyNoFlags(a, b);
#endif
return Mul128BitLogic(a, b);
}
[MethodImpl(256)]
internal static ulong Mul128BitLogic(ulong a, ulong b)
{
var au = a >> 32;
var ad = a & 0xFFFFFFFF;
var bu = b >> 32;
var bd = b & 0xFFFFFFFF;
var l = ad * bd;
var m1 = au * bd;
var m2 = ad * bu;
var h = au * bu;
var lu = l >> 32;
var m1d = m1 & 0xFFFFFFFF;
var m2d = m2 & 0xFFFFFFFF;
var c = m1d + m2d + lu;
return h + (m1 >> 32) + (m2 >> 32) + (c >> 32);
}
}
public static class Butterfly<T> where T : struct, IStaticMod
{
[EditorBrowsable(EditorBrowsableState.Never)]
public static readonly StaticModInt<T>[] sumE = CalcurateSumE();
[EditorBrowsable(EditorBrowsableState.Never)]
public static readonly StaticModInt<T>[] sumIE = CalcurateSumIE();
[MethodImpl(256)]
public static void Calculate(Span<StaticModInt<T>> a)
{
CheckPow2(a.Length);
var n = a.Length;
var h = InternalBit.CeilPow2(n);
var regLength = Vector<uint>.Count;
#if !NETCOREAPP3_0_OR_GREATER
var copyTmp = new uint[regLength];
#endif
var modV = new Vector<uint>(default(T).Mod);
for (int ph = 1; ph <= h; ph++)
{
int w = 1 << (ph - 1);
int p = 1 << (h - ph);
var now = StaticModInt<T>.Raw(1);
for (int s = 0; s < w; s++)
{
int offset = s << (h - ph + 1);
var ls = a.Slice(offset, p);
var rs = a.Slice(offset + p, p);
if (p < regLength)
{
for (int i = 0; i < p; i++)
{
var l = ls[i];
var r = rs[i] * now;
ls[i] = l + r;
rs[i] = l - r;
}
}
else
{
foreach (ref var r in rs)
{
r *= now;
}
var lu = MemoryMarshal.Cast<StaticModInt<T>, uint>(ls);
var ru = MemoryMarshal.Cast<StaticModInt<T>, uint>(rs);
for (int i = 0; i < lu.Length; i += regLength)
{
var luSliced = lu.Slice(i);
var ruSliced = ru.Slice(i);
var u = new Vector<uint>(luSliced);
var v = new Vector<uint>(ruSliced);
var add = u + v;
var sub = u - v;
var ge = Vector.GreaterThanOrEqual(add, modV);
add = Vector.ConditionalSelect(ge, add - modV, add);
ge = Vector.GreaterThanOrEqual(sub, modV);
sub = Vector.ConditionalSelect(ge, sub + modV, sub);
#if !NETCOREAPP3_0_OR_GREATER
add.CopyTo(copyTmp);
copyTmp.CopyTo(luSliced);
sub.CopyTo(copyTmp);
copyTmp.CopyTo(ruSliced);
#else
add.CopyTo(luSliced);
sub.CopyTo(ruSliced);
#endif
}
}
now *= sumE[InternalBit.Bsf(~(uint)s)];
}
}
}
[MethodImpl(256)]
public static void CalculateInv(Span<StaticModInt<T>> a)
{
CheckPow2(a.Length);
var n = a.Length;
var h = InternalBit.CeilPow2(n);
var regLength = Vector<uint>.Count;
#if !NETCOREAPP3_0_OR_GREATER
var copyTmp = new uint[regLength];
#endif
var modV = new Vector<uint>(default(T).Mod);
for (int ph = h; ph >= 1; ph--)
{
int w = 1 << (ph - 1);
int p = 1 << (h - ph);
var iNow = StaticModInt<T>.Raw(1);
for (int s = 0; s < w; s++)
{
int offset = s << (h - ph + 1);
var ls = a.Slice(offset, p);
var rs = a.Slice(offset + p, p);
if (p < regLength)
{
for (int i = 0; i < p; i++)
{
var l = ls[i];
var r = rs[i];
ls[i] = l + r;
rs[i] = StaticModInt<T>.Raw(
(int)((ulong)(default(T).Mod + l.Value - r.Value) * (ulong)iNow.Value % default(T).Mod));
}
}
else
{
var lu = MemoryMarshal.Cast<StaticModInt<T>, uint>(ls);
var ru = MemoryMarshal.Cast<StaticModInt<T>, uint>(rs);
for (int i = 0; i < lu.Length; i += regLength)
{
var luSliced = lu.Slice(i);
var ruSliced = ru.Slice(i);
var u = new Vector<uint>(luSliced);
var v = new Vector<uint>(ruSliced);
var add = u + v;
var sub = u - v;
var ge = Vector.GreaterThanOrEqual(add, modV);
add = Vector.ConditionalSelect(ge, add - modV, add);
sub += modV;
#if !NETCOREAPP3_0_OR_GREATER
add.CopyTo(copyTmp);
copyTmp.CopyTo(luSliced);
sub.CopyTo(copyTmp);
copyTmp.CopyTo(ruSliced);
#else
add.CopyTo(luSliced);
sub.CopyTo(ruSliced);
#endif
}
foreach (ref var r in rs)
{
r *= iNow;
}
}
iNow *= sumIE[InternalBit.Bsf(~(uint)s)];
}
}
}
[EditorBrowsable(EditorBrowsableState.Never)]
public static StaticModInt<T>[] CalcurateSumE()
{
int g = InternalMath.PrimitiveRoot<T>();
int cnt2 = InternalBit.Bsf(default(T).Mod - 1);
var e = new StaticModInt<T>(g).Pow((default(T).Mod - 1) >> cnt2);
var ie = e.Inv();
var sumE = new StaticModInt<T>[30];
Span<StaticModInt<T>> es =
#if !NETCOREAPP3_0_OR_GREATER
new
#else
stackalloc
#endif
StaticModInt<T>[cnt2 - 1];
Span<StaticModInt<T>> ies =
#if !NETCOREAPP3_0_OR_GREATER
new
#else
stackalloc
#endif
StaticModInt<T>[cnt2 - 1];
for (int i = es.Length - 1; i >= 0; i--)
{
es[i] = e;
ies[i] = ie;
e *= e;
ie *= ie;
}
var now = StaticModInt<T>.Raw(1);
for (int i = 0; i <= cnt2 - 2; i++)
{
sumE[i] = es[i] * now;
now *= ies[i];
}
return sumE;
}
[EditorBrowsable(EditorBrowsableState.Never)]
public static StaticModInt<T>[] CalcurateSumIE()
{
int g = InternalMath.PrimitiveRoot<T>();
int cnt2 = InternalBit.Bsf(default(T).Mod - 1);
var e = new StaticModInt<T>(g).Pow((default(T).Mod - 1) >> cnt2);
var ie = e.Inv();
var sumIE = new StaticModInt<T>[30];
Span<StaticModInt<T>> es =
#if !NETCOREAPP3_0_OR_GREATER
new
#else
stackalloc
#endif
StaticModInt<T>[cnt2 - 1];
Span<StaticModInt<T>> ies =
#if !NETCOREAPP3_0_OR_GREATER
new
#else
stackalloc
#endif
StaticModInt<T>[cnt2 - 1];
for (int i = es.Length - 1; i >= 0; i--)
{
es[i] = e;
ies[i] = ie;
e *= e;
ie *= ie;
}
var now = StaticModInt<T>.Raw(1);
for (int i = 0; i <= cnt2 - 2; i++)
{
sumIE[i] = ies[i] * now;
now *= es[i];
}
return sumIE;
}
[Conditional("ATCODER_CONTRACT")]
private static void CheckPow2(int n)
{
if (BitOperations.PopCount((uint)n) != 1)
{
throw new ArgumentException("配列長は2のべき乗でなければなりません。");
}
}
}
public class Barrett
{
public readonly uint Mod;
public readonly ulong IM;
public Barrett(uint m)
{
Mod = m;
IM = unchecked((ulong)-1) / m + 1;
}
[MethodImpl(256)]
public uint Mul(uint a, uint b) => Reduce((ulong)a * b);
[MethodImpl(256)]
public uint Reduce(ulong z)
{
var x = InternalMath.Mul128Bit(z, IM);
var v = unchecked((uint)(z - x * Mod));
if (Mod <= v) v += Mod;
return v;
}
[MethodImpl(256)]
public uint Pow(long x, long n)
{
Contract.Assert(0 <= n, $"{nameof(n)} must be positive.");
if (Mod == 1) return 0;
uint r = 1, y = (uint)InternalMath.SafeMod(x, Mod);
while (n > 0)
{
if ((n & 1) != 0) r = Mul(r, y);
y = Mul(y, y);
n >>= 1;
}
return r;
}
}