結果

問題 No.8120 Aoki's Present for Takahashi
ユーザー tobisatis
提出日時 2025-04-01 22:56:23
言語 C#
(.NET 8.0.404)
結果
AC  
実行時間 465 ms / 2,000 ms
コード長 7,652 bytes
コンパイル時間 9,586 ms
コンパイル使用メモリ 173,676 KB
実行使用メモリ 243,496 KB
最終ジャッジ日時 2025-04-01 23:17:37
合計ジャッジ時間 19,337 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 1
other AC * 20
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 (111 ミリ秒)。
  main -> /home/judge/data/code/bin/Release/net8.0/main.dll
  main -> /home/judge/data/code/bin/Release/net8.0/publish/

ソースコード

diff # 

#nullable enable

using System.Numerics;

    // void init(long long p) {  // 動的計画法で前処理
    //     com.assign(p, vector<long long>(p));
    //     com[0][0] = 1;
    //     for (int i = 1; i < p; i++) {
    //         com[i][0] = 1;
    //         for (int j = i; j > 0; j--) {
    //             com[i][j] = (com[i - 1][j - 1] + com[i - 1][j]) % p;
    //         }
    //     }
    // }

const int p = 443;

void Run()
{
    var (t2, t1) = (Int(), Int());
    var nck = new long[p, p];
    nck[0, 0] = 1;
    for (var i = 1; i < p; i++)
    {
        nck[i, 0] = 1;
        for (var j = i; j > 0; j--)
        {
            nck[i, j] = nck[i - 1, j - 1] + nck[i - 1, j];
            nck[i, j] %= p;
        }
    }
    var ans = new long[t1];
    for (var i = 0; i < t1; i++)
    {
        var n = Int();
        var m = Int();
        n = Math.Min(n, m - n);
        ans[i] = m.C(n);
        {
            var pk = 1L;
            while (m > 0)
            {
                pk *= nck[m % p, n % p];
                pk %= p;
                m /= p;
                n /= p;
            }
            var q = Extensions.ChineseRemainderTheorem((ans[i], ModInt.Mod), (pk, p));
            ans[i] = q!.Value.r;
        }
    }
    for (var i = 1; i <= t1; i++) Out(i == t2 ? -1 : ans[i - 1]);
}

#region
AtCoderIO _io_;
var _backend_ = new StandardIOBackend();
_io_ = new(){ Backend = _backend_ };
Run();
_backend_.Flush();

string String() => _io_.Next();
int Int() => int.Parse(String());
void Out(object? x, string? sep = null) => _io_.Out(x, sep);

class AtCoderIO
{
    public required StandardIOBackend Backend { get; init; }

    Memory<string> _input = Array.Empty<string>();
    int _iter = 0;
    public string Next()
    {
        while (_iter >= _input.Length) (_input, _iter) = (Backend.ReadLine().Split(' '), 0);
        return _input.Span[_iter++];
    }

    public void Out(object? x, string? separator = null)
    {
        if (x == null) return;
        separator ??= Environment.NewLine;
        if (x is System.Collections.IEnumerable a and not string)
        {
            var objects = a.Cast<object>();
            if (separator == Environment.NewLine && !objects.Any()) return;
            x = string.Join(separator, objects);
        }
        Backend.WriteLine(x);
    }
}

class StandardIOBackend
{
    readonly StreamReader _sr = new(Console.OpenStandardInput());
    readonly StreamWriter _sw = new(Console.OpenStandardOutput()) { AutoFlush = false };
    public string ReadLine() => _sr.ReadLine()!;
    public void WriteLine(object? value) => _sw.WriteLine(value);
    public void Flush() => _sw.Flush();
}
#endregion

static class Extensions
{
    public static T[] Repeat<T>(this int time, Func<T> F) => Enumerable.Range(0, time).Select(_ => F()).ToArray();

    public static (long r, long m)? ChineseRemainderTheorem(params (long r, long m)[] conditions)
    {
        static (long d, long x, long y) ExtendedGcd(long a, long b)
        {
            if (b == 0) return (a, 1, 0);
            var (d, x, y) = ExtendedGcd(b, a % b);
            return (d, y, x - a / b * y);
        }
        var (R, M) = (0L, 1L);
        for (var i = 0; i < conditions.Length; i++)
        {
            var (r, m) = conditions[i];
            if (m <= 0) return null;
            r %= m;
            if (r < 0) r += m;
            var (d, x, _) = ExtendedGcd(M, m);
            if ((r - R) % d != 0) return null;
            var p = m / d;
            R += M * ((r - R) / d * x % p);
            M *= p;
            R %= M;
            if (R < 0) R += M;
        }
        return (R, M);
    }
}

readonly record struct ModInt
{
    public const int Mod = 2253371;
    int V { get; init; }
    public ModInt(long value)
    {
        var v = value % Mod;
        if (v < 0) v += Mod;
        V = (int)v;
    }
    static ModInt New(int value) => new(){ V = value };

    public static implicit operator ModInt(long v) => new(v);
    public static implicit operator int(ModInt modInt) => modInt.V;

    public static ModInt AdditiveIdentity => New(0);
    public static ModInt operator +(ModInt a, ModInt b)
    {
        var v = a.V + b.V;
        if (v >= Mod) v -= Mod;
        return New(v);
    }
    public ModInt AdditiveInverse()
    {
        if (V == 0) return AdditiveIdentity;
        return New(Mod - V);
    }
    public static ModInt operator -(ModInt a, ModInt b)
    {
        var v = a.V - b.V;
        if (v < 0) v += Mod;
        return New(v);
    }

    public static ModInt MultiplicativeIdentity => New(1);
    public static ModInt operator *(ModInt a, ModInt b) => New((int)((long)a.V * b.V % Mod));
    public ModInt MultiplicativeInverse()
    {
        if (V == 0) throw new DivideByZeroException();
        var (d, x, _) = ExtendedGCD(V, Mod);
        if (d > 1) throw new DivideByZeroException();
        return x;
    }
    public static ModInt operator /(ModInt a, ModInt b) => a * b.MultiplicativeInverse();

    static long Power(long v, ulong p, long mod)
    {
        var (res, k) = (1L, v);
        while (p > 0)
        {
            if ((p & 1) > 0) res = res * k % mod;
            k = k * k % mod;
            p >>= 1;
        }
        return res;
    }
    public ModInt Power(long p) => p < 0 ? (MultiplicativeIdentity / V).Power(-p) : Power(V, (ulong)p, Mod);

    static (long d, long x, long y) ExtendedGCD(long a, long b)
    {
        var (x0, y0, x1, y1) = (1L, 0L, 0L, 1L);
        while (b != 0)
        {
            var q = a / b;
            (a, b) = (b, a - q * b);
            (x0, y0, x1, y1) = (x1, y1, x0 - q * x1, y0 - q * y1);
        }
        return (a, x0, y0);
    }

    public override string ToString() => V.ToString();
}

static class FactorialExtensions
{
    public static ModInt Factorial(this int value)
    {
        Extend(value);
        return value < 0 ? _inv.Span[-value] : _fac.Span[value];
    }
    public static ModInt P(this int n, int r)
    {
        if (r < 0 || r > n) return 0;
        if (n <= MaxN) return Factorial(n) * Factorial(r - n);
        ModInt res = 1;
        for (var i = 0; i < r; i++) res *= n - i;
        return res;
    }
    public static ModInt C(this int n, int r)
    {
        if (r < 0 || r > n) return 0;
        r = Math.Min(r, n - r);
        return P(n, r) * Factorial(-r);
    }
    public static ModInt H(this int n, int r) => C(r + n - 1, r);

    public static ModInt ModIntInverse(this int n)
    {
        if (n == 0) throw new DivideByZeroException();
        if (n < 0) return ModIntInverse(-n).AdditiveInverse();
        if (n > MaxN) return ((ModInt)n).MultiplicativeInverse();
        return Factorial(n - 1) * Factorial(-n);
    }

    // [x^k](1-x)^-n = nHk
    public static ModInt[] NegativeBinomialSeries(long n, int m)
    {
        var res = new ModInt[m + 1];
        res[0] = 1;
        for (var i = 1; i <= m; i++) res[i] = res[i - 1] * (n - 1 + i) * ModIntInverse(i);
        return res;
    }

    const int MaxN = (1 << 24) - 1;
    static Memory<ModInt> _fac = new ModInt[]{ 1 };
    static Memory<ModInt> _inv = new ModInt[]{ 1 };
    static void Extend(int q)
    {
        var l = _fac.Length;
        if (q < 0) q = -q;
        if (q < l || MaxN < q) return;
        while (l <= q) l = 2253370;
        var fac = new ModInt[l];
        var inv = new ModInt[l];
        var sf = fac.AsSpan();
        sf[0] = 1;
        for (var i = 1; i < sf.Length; i++) sf[i] = sf[i - 1] * i;
        var si = inv.AsSpan();
        si[l - 1] = sf[l - 1].Power(-1);
        for (var i = si.Length - 1; i > 0; i--) si[i - 1] = si[i] * i;
        (_fac, _inv) = (fac, inv);
    }
}
0