結果

問題 No.2896 Monotonic Prime Factors
ユーザー tobisatistobisatis
提出日時 2024-09-20 23:21:27
言語 C#
(.NET 8.0.203)
結果
AC  
実行時間 273 ms / 2,000 ms
コード長 6,999 bytes
コンパイル時間 15,080 ms
コンパイル使用メモリ 165,776 KB
実行使用メモリ 200,436 KB
最終ジャッジ日時 2024-09-20 23:21:53
合計ジャッジ時間 17,783 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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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 60 ms
30,592 KB
testcase_01 AC 60 ms
30,592 KB
testcase_02 AC 61 ms
30,840 KB
testcase_03 AC 64 ms
30,832 KB
testcase_04 AC 161 ms
58,880 KB
testcase_05 AC 268 ms
85,112 KB
testcase_06 AC 244 ms
71,296 KB
testcase_07 AC 161 ms
58,880 KB
testcase_08 AC 161 ms
58,740 KB
testcase_09 AC 273 ms
85,240 KB
testcase_10 AC 151 ms
46,464 KB
testcase_11 AC 101 ms
37,624 KB
testcase_12 AC 75 ms
33,368 KB
testcase_13 AC 152 ms
47,988 KB
testcase_14 AC 167 ms
52,736 KB
testcase_15 AC 70 ms
32,000 KB
testcase_16 AC 109 ms
41,984 KB
testcase_17 AC 94 ms
36,864 KB
testcase_18 AC 183 ms
62,976 KB
testcase_19 AC 96 ms
200,436 KB
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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 (108 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 # 

namespace AtCoder;

#nullable enable

using System.Numerics;

readonly record struct ModInt :
    IEqualityOperators<ModInt, ModInt, bool>,
    IAdditiveIdentity<ModInt, ModInt>,
    IAdditionOperators<ModInt, ModInt, ModInt>,
    IUnaryNegationOperators<ModInt, ModInt>,
    ISubtractionOperators<ModInt, ModInt, ModInt>,
    IMultiplicativeIdentity<ModInt, ModInt>,
    IMultiplyOperators<ModInt, ModInt, ModInt>,
    IDivisionOperators<ModInt, ModInt, ModInt>
{
    int V { get; init; }
    public const int Mod = 998244353;
    public ModInt(long value)
    {
        var v = value % Mod;
        if (v < 0) v += Mod;
        V = (int)v;
    }
    ModInt(int value) { V = value; }

    public static implicit operator ModInt(long v) => new(v);
    public static implicit operator int(ModInt modInt) => modInt.V;
    public static ModInt operator +(ModInt a, ModInt b)
    {
        var v = a.V + b.V;
        if (v >= Mod) v -= Mod;
        return new(v);
    }
    public static ModInt operator -(ModInt a) => new(a.V == 0 ? 0 : Mod - a.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 operator *(ModInt a, ModInt b) => new((int)((long)a.V * b.V % Mod));
    public static ModInt operator /(ModInt a, ModInt b)
    {
        if (b == 0) throw new DivideByZeroException();
        var (d, x, _) = ExtendedGcd(b.V, Mod);
        if (d > 1) throw new DivideByZeroException();
        return x * a.V;
    }

    public ModInt Power(long p)
    {
        if (p < 0) return (MultiplicativeIdentity / V).Power(-p);
        long res = 1;
        long k = V;
        while (p > 0)
        {
            if ((p & 1) > 0) res = res * k % Mod;
            k = k * k % Mod;
            p >>= 1;
        }
        return res;
    }

    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);
    }

    public static ModInt AdditiveIdentity => new(0);
    public static ModInt MultiplicativeIdentity => new(1);

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

static class FactorialExtensions
{
    static ModInt[] fac = Array.Empty<ModInt>();
    static ModInt[] inv = Array.Empty<ModInt>();
    const uint Capacity = 1 << 24;
    
    static void Resize(uint n)
    {
        if (n < fac.Length) return;
        var s = 1;
        while (s < n && s < Capacity) s <<= 1;
        fac = new ModInt[s + 1];
        fac[0] = 1;
        for (var i = 1; i <= s; i++) fac[i] = fac[i - 1] * i;
        inv = new ModInt[s + 1];
        inv[s] = fac[0] / fac[s];
        for (var i = s; i > 0; i--) inv[i - 1] = inv[i] * i;
    }

    public static ModInt Factorial(this int n) { Resize((uint)Math.Abs(n)); return n < 0 ? inv[-n] : fac[n]; }

    public static ModInt C(this int n, int r)
    {
        if (r < 0 || n < r) return 0;
        if (n <= Capacity) return Factorial(n) * Factorial(r - n) * Factorial(-r);
        if (n - r < r) return C(n, n - r);
        ModInt res = 1;
        for (var i = n; i > n - r; i--) res *= i;
        return res * Factorial(-r);
    }
    public static ModInt P(this int n, int r) => C(n, r) * Factorial(r);
    public static ModInt H(this int n, int r) => C(n + r - 1, r);
}

class Prime
{
    readonly int[] sieve;
    public readonly List<int> Primes = new();

    public Prime(int n)
    {
        if (n <= 3) n = 3;
        sieve = new int[n + 1];
        var (d, i, primes) = (2, 5, Primes);
        primes.Add(2);
        primes.Add(3);
        var span = sieve.AsSpan();
        span[1] = 1;
        for (var j = 2; j <= n; j += 2) span[j] = 2;
        for (var j = 3; j <= n; j += 3) span[j] = 3;
        while (i <= n)
        {
            if (span[i] == 0)
            {
                primes.Add(i);
                for (var j = i; j <= n; j += i) span[j] = i;
            }
            i += d;
            d ^= 6;
        }
    }

    public bool IsPrime(int x)
    {
        if (x < 2) return false;
        if (x < sieve.Length) return sieve[x] == x;
        foreach (long p in Primes)
        {
            if (p * p > x) return true;
            if (x % p == 0) return false;
        }
        throw new Exception();
    }

    // descending
    public List<int> Factorize(int x)
    {
        var factors = new List<int>();
        while (sieve[x] > 1) { factors.Add(sieve[x]); x /= sieve[x]; }
        return factors;
    }

    public List<int> Divisors(int x)
    {
        var factors = Factorize(x);
        var powerLists = new List<List<int>>();
        var last = 1;
        foreach (var factor in factors)
        {
            if (factor != last)
            {
                powerLists.Add(new List<int>(new int[] { 1 }));
                last = factor;
            }
            var powers = powerLists[^1];
            powers.Add(powers[^1] * factor);
        }
        var divisors = new List<int>();
        void Enumerate(int index, int divisor)
        {
            if (index == powerLists.Count) { divisors.Add(divisor); return; }
            foreach (var power in powerLists[index]) Enumerate(index + 1, divisor * power);
        }
        Enumerate(0, 1);
        return divisors;
    }
}

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

class AtCoder
{
    object? Solve()
    {
        var q = Int();
        var prime = new Prime(100000);
        var ans = new long[q];
        var k = 0;
        for (var i = 0; i < q; i++)
        {
            var a = Int();
            var b = Int();
            k += prime.Factorize(a).Count;
            ans[i] = (k - 1).C(b - 1);
        }
        Out(ans);
        return null;
    }

    public static void Main() => new AtCoder().Run();
    public void Run()
    {
        var res = Solve();
        if (res != null)
        {
            if (res is bool yes) res = yes ? "Yes" : "No";
            sw.WriteLine(res);
        }
        sw.Flush();
    }

    string[] input = Array.Empty<string>();
    int iter = 0;
    readonly StreamWriter sw = new(Console.OpenStandardOutput()) { AutoFlush = false };

    string String()
    {
        while (iter >= input.Length) (input, iter) = (Console.ReadLine()!.Split(' '), 0);
        return input[iter++];
    }
    T Input<T>() where T : IParsable<T> => T.Parse(String(), null);
    int Int() => Input<int>();
    void Out(object? x, string? separator = null)
    {
        separator ??= Environment.NewLine;
        if (x is System.Collections.IEnumerable obj and not string)
        {
            var firstLine = true;
            foreach (var item in obj)
            {
                if (!firstLine) sw.Write(separator);
                firstLine = false;
                sw.Write(item);
            }
        }
        else sw.Write(x);
        sw.WriteLine();
    }
}
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