結果

問題 No.2613 Sum of Combination
ユーザー KumaTachiRenKumaTachiRen
提出日時 2024-01-20 14:48:40
言語 C#
(.NET 8.0.203)
結果
AC  
実行時間 658 ms / 4,500 ms
コード長 31,033 bytes
コンパイル時間 8,680 ms
コンパイル使用メモリ 168,152 KB
実行使用メモリ 209,900 KB
最終ジャッジ日時 2024-09-28 05:35:19
合計ジャッジ時間 26,776 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 44 ms
23,524 KB
testcase_01 AC 42 ms
23,296 KB
testcase_02 AC 92 ms
29,156 KB
testcase_03 AC 44 ms
23,680 KB
testcase_04 AC 43 ms
23,424 KB
testcase_05 AC 42 ms
23,296 KB
testcase_06 AC 44 ms
23,552 KB
testcase_07 AC 43 ms
23,552 KB
testcase_08 AC 61 ms
25,472 KB
testcase_09 AC 56 ms
25,344 KB
testcase_10 AC 42 ms
23,516 KB
testcase_11 AC 58 ms
25,444 KB
testcase_12 AC 58 ms
25,472 KB
testcase_13 AC 98 ms
29,312 KB
testcase_14 AC 91 ms
29,312 KB
testcase_15 AC 87 ms
29,312 KB
testcase_16 AC 91 ms
29,568 KB
testcase_17 AC 91 ms
29,440 KB
testcase_18 AC 91 ms
29,440 KB
testcase_19 AC 92 ms
29,568 KB
testcase_20 AC 64 ms
25,472 KB
testcase_21 AC 57 ms
25,472 KB
testcase_22 AC 104 ms
30,208 KB
testcase_23 AC 647 ms
44,492 KB
testcase_24 AC 650 ms
44,560 KB
testcase_25 AC 638 ms
42,872 KB
testcase_26 AC 651 ms
45,852 KB
testcase_27 AC 354 ms
44,416 KB
testcase_28 AC 650 ms
45,612 KB
testcase_29 AC 643 ms
45,256 KB
testcase_30 AC 655 ms
45,812 KB
testcase_31 AC 652 ms
45,000 KB
testcase_32 AC 651 ms
44,732 KB
testcase_33 AC 646 ms
46,812 KB
testcase_34 AC 641 ms
46,524 KB
testcase_35 AC 649 ms
46,836 KB
testcase_36 AC 650 ms
46,812 KB
testcase_37 AC 656 ms
46,704 KB
testcase_38 AC 654 ms
45,664 KB
testcase_39 AC 653 ms
45,460 KB
testcase_40 AC 645 ms
45,580 KB
testcase_41 AC 646 ms
45,764 KB
testcase_42 AC 658 ms
45,656 KB
testcase_43 AC 643 ms
46,836 KB
testcase_44 AC 634 ms
46,320 KB
testcase_45 AC 43 ms
23,424 KB
testcase_46 AC 43 ms
23,552 KB
testcase_47 AC 43 ms
23,552 KB
testcase_48 AC 44 ms
23,552 KB
testcase_49 AC 44 ms
23,936 KB
testcase_50 AC 530 ms
46,176 KB
testcase_51 AC 528 ms
209,900 KB
権限があれば一括ダウンロードができます
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 (89 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

diff # 

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.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()
    {
        long n = rl, p = ri;
        long r = MathLib.PrimitiveRoot((int)p);
        var log = new int[p];
        {
            long x = 1;
            for (int i = 0; i < p - 1; i++)
            {
                log[x] = i;
                x = x * r % p;
            }
        }

        long Pow(long x, long n)
        {
            long r = 1;
            while (n > 0)
            {
                if (n % 2 == 1) r = r * x % p;
                x = x * x % p;
                n /= 2;
            }
            return r;
        }
        long Inv(long x) => Pow(x, p - 2);

        var fact = new long[p];
        fact[0] = 1;
        for (int i = 1; i < p; i++) fact[i] = fact[i - 1] * i % p;
        var ifact = new long[p];
        ifact[^1] = Inv(fact[^1]);
        for (int i = (int)p - 1; i > 0; i--) ifact[i - 1] = ifact[i] * i % p;

        long Binom(long n, long r) => 0 <= r && r <= n ? fact[n] * ifact[r] * ifact[n - r] % p : 0;

        var f = new ModInt[p - 1];
        f[0] = 1;
        for (long m = n; m > 0; m /= p)
        {
            var g = new ModInt[p - 1];
            long v = m % p;
            for (int i = 0; i <= v; i++) g[log[Binom(v, i)]]++;
            g = MathLib.Convolution(f, g);
            for (int i = 0; i < p - 1; i++) f[i] = g[i];
            for (int i = (int)p - 1; i < g.Length; i++) f[i - (p - 1)] += g[i];
        }
        ModInt ans = 0;
        {
            long x = 1;
            for (int i = 0; i < p - 1; i++)
            {
                ans += x * f[i];
                x = x * r % p;
            }
        }
        Write(ans);
    }

    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(long x) { x = (x & 0x5555555555555555L) + ((x >> 1) & 0x5555555555555555L); x = (x & 0x3333333333333333L) + ((x >> 2) & 0x3333333333333333L); x = (x & 0x0f0f0f0f0f0f0f0fL) + ((x >> 4) & 0x0f0f0f0f0f0f0f0fL); x = (x & 0x00ff00ff00ff00ffL) + ((x >> 8) & 0x00ff00ff00ff00ffL); x = (x & 0x0000ffff0000ffffL) + ((x >> 16) & 0x0000ffff0000ffffL); x = (x & 0x00000000ffffffffL) + ((x >> 32) & 0x00000000ffffffffL); 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 uint Gcd(uint a, uint 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 ulong Gcd(ulong a, ulong 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>> 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) => new StaticModInt<T>((uint)((ulong)lhs._v * Inv(rhs._v) % op.Mod)); [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() => new StaticModInt<T>(Inv(_v)); [MethodImpl(256)] static ulong Inv(ulong x) { long u = op.Mod, xu = 1, yu = 0, v = (long)x, xv = 0, yv = 1; while (v != 0) { long w = SafeMod(u, v); long q = (u - w) / v; long xw = xu - xv * q; long yw = yu - yv * q; u = v; xu = xv; yu = yv; v = w; xv = xw; yv = yw; } return (ulong)(yu < 0 ? yu + op.Mod : yu); } [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 partial class MathLib { public static int PrimitiveRoot(int p) { Debug.Assert(p >= 2); if (p == 2) return 1; if (p == 3) return 2; if (p == 5) return 2; int q = p - 1; var pf = new List<int>(); for (int x = 2; (long)x * x <= q; x += (x & 1) + 1) { if (q % x != 0) continue; pf.Add(x); while (q % x == 0) q /= x; } if (q > 1) pf.Add(q); q = p - 1; var rnd = new XORShift.XORShift32(); while (true) { int r = (int)(rnd.Next() % (p - 2)) + 2; bool ok = true; for (int i = 0; ok && i < pf.Count; i++) { int n = q / pf[i]; long x = r, y = 1; while (n > 0) { if (n % 2 == 1) y = y * x % p; x = x * x % p; n /= 2; } if (y == 1) ok = false; } if (ok) return r; } } }
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) { var temp = a; a = b; b = temp; } 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 class XORShift { public class XORShift32 { uint x; public XORShift32() { x = 2463534242; } public uint Next() { x ^= x << 13; x ^= x >> 17; x ^= x << 5; return x; } } public class XORShift64 { ulong x; public XORShift64() { x = 88172645463325252; } public ulong Next() { x ^= x << 13; x ^= x >> 7; x ^= x << 17; return x; } } }
public static class InternalBit { [MethodImpl(256)] public static uint ExtractLowestSetBit(int n) { if (System.Runtime.Intrinsics.X86.Bmi1.IsSupported) return System.Runtime.Intrinsics.X86.Bmi1.ExtractLowestSetBit((uint)n); return (uint)(n & -n); } [MethodImpl(256)] public static int Bsf(uint n) { 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 (primitiveRootsCache.TryGetValue(m, out var p)) return p; return primitiveRootsCache[m] = PrimitiveRootCalculate<TMod>(); } 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 (System.Runtime.Intrinsics.X86.Bmi2.X64.IsSupported) return System.Runtime.Intrinsics.X86.Bmi2.X64.MultiplyNoFlags(a, b); 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; 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); add.CopyTo(luSliced); sub.CopyTo(ruSliced); } } 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; 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; add.CopyTo(luSliced); sub.CopyTo(ruSliced); } 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 = stackalloc StaticModInt<T>[cnt2 - 1]; Span<StaticModInt<T>> ies = stackalloc 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 = stackalloc StaticModInt<T>[cnt2 - 1]; Span<StaticModInt<T>> ies = stackalloc 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; } }
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