#845274 (C#) No.125 悪の花弁

• 問題: No.125 悪の花弁
• ユーザー: KumaTachiRen
• 提出日時: 2023-03-03 17:45:44
• 言語: C# (.NET 8.0.203)
• 結果: AC
• 実行時間: 342 ms / 5,000 ms
• コード長: 11,636 bytes
• コンパイル時間: 8,254 ms
• コンパイル使用メモリ: 167,316 KB
• 実行使用メモリ: 209,444 KB
• 最終ジャッジ日時: 2024-09-17 22:08:05
• 合計ジャッジ時間: 10,364 ms
• ジャッジサーバーID （参考情報）: judge4 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	254 ms; 44,288 KB
testcase_01	AC	165 ms; 43,392 KB
testcase_02	AC	209 ms; 49,920 KB
testcase_03	AC	214 ms; 50,176 KB
testcase_04	AC	342 ms; 51,328 KB
testcase_05	AC	205 ms; 209,444 KB

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 (100 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.Diagnostics;
using System;
using System.Linq;
using System.Numerics;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Text;
using System.Runtime.CompilerServices;
using static Functions;

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 k = ri;
        var c = new int[k];
        for (int i = 0; i < k; i++) c[i] = ri;
        int g = c[0];
        for (int i = 0; i < k; i++) g = Gcd(g, c[i]);
        var dp = new ModInt[g + 1];
        int s = c.Sum();
        var f = new ModFact(s);
        for (int d = 1; d <= g; d++)
        {
            if (g % d != 0) continue;
            dp[d] = f.Fact(s / d);
            for (int i = 0; i < k; i++) dp[d] *= f.FactInv(c[i] / d);
        }
        for (int i = g; i > 0; i--)
            for (int j = i * 2; j <= g; j += i)
                dp[i] -= dp[j];
        ModInt ans = 0;
        for (int i = 1; i <= g; i++) ans += dp[i] * f.Inv(s / i);
        Write(ans);
    }

    const long INF = 1L << 60;
    int ri { get { return (int)sc.Integer(); } }
    long rl { get { return sc.Integer(); } }
    ulong rul { get { return sc.UInteger(); } }
    double rd { get { return sc.Double(); } }
    string rs { get { return sc.Scan(); } }
    string rline { get { return sc.Line(); } }
    public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());

    T[] RepArray<T>(T t, int count) => Enumerable.Repeat(t, count).ToArray();
    void WriteJoin<T>(string s, IEnumerable<T> t) { Console.WriteLine(string.Join(s, t)); }
    void WriteMat<T>(T[,] a)
    {
        int sz1 = a.GetLength(0);
        int sz2 = a.GetLength(1);
        for (int i = 0; i < sz1; i++)
        {
            var s = new List<string>();
            for (int j = 0; j < sz2; j++) s.Add(a[i, j].ToString());
            WriteJoin(" ", s);
        }
    }
    void WriteMax(params long[] x) => Console.WriteLine(x.Max());
    void WriteMin(params long[] x) => Console.WriteLine(x.Min());
    void Write(object t) => Console.WriteLine(t.ToString());
    void Write(string str, object arg1) => Console.WriteLine(str, arg1);
    void Write(string str, object arg1, object arg2) => Console.WriteLine(str, arg1, arg2);
    void Write(string str, object arg1, object arg2, object arg3) => Console.WriteLine(str, arg1, arg2, arg3);
    void Write(string str, params object[] arg) => Console.WriteLine(str, arg);
    void WriteFlush(object t) { Console.WriteLine(t.ToString()); Console.Out.Flush(); }
    void WriteError(object t) { Console.Error.WriteLine(t.ToString()); }
    void YN(bool t) { Console.WriteLine(t ? "YES" : "NO"); }
    void Yn(bool t) { Console.WriteLine(t ? "Yes" : "No"); }
    void yn(bool t) { Console.WriteLine(t ? "yes" : "no"); }
}

public static class Functions
{
    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;
    }
    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;
    }
    public static int Ctz(long x)
    {
        if (x == 0) return -1;
        return Popcount((ulong)((x & -x) - 1));
    }
    public static int SafeMod(int x, int m)
    {
        int r = x % m;
        return r < 0 ? r + m : r;
    }
    public static long SafeMod(long x, long m)
    {
        long r = x % m;
        return r < 0 ? r + m : r;
    }
    public static int Sign(long x) => x == 0 ? 0 : (x < 0 ? -1 : 1);
    public static int DigitSum(long n, int d = 10) { long s = 0; while (n > 0) { s += n % d; n /= d; } return (int)s; }
    public static long Floor(long a, long b) => a >= 0 ? a / b : (a + 1) / b - 1;
    public static long Ceil(long a, long b) => a > 0 ? (a - 1) / b + 1 : a / b;
    public static int Gcd(int a, int b) => b == 0 ? a : Gcd(b, a % b);
    public static long Gcd(long a, long b) => b == 0 ? a : Gcd(b, a % b);
    public static void Swap(ref int x, ref int y) { x ^= y; y ^= x; x ^= y; }
    public static void Swap(ref long x, ref long y) { x ^= y; y ^= x; x ^= y; }
    public static void Swap<T>(ref T x, ref T y) { T t = y; y = x; x = t; }
    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);
    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);
    public static void Chmin<T>(ref T x, T y) where T : IComparable<T> { if (x.CompareTo(y) > 0) x = y; }
    public static void Chmax<T>(ref T x, T y) where T : IComparable<T> { if (x.CompareTo(y) < 0) x = y; }
    public static int LowerBound<T>(in T[] arr, Func<T, int> comp, int l = -1, int r = -1)
    {
        if (arr.Length == 0) return -1;
        if (l == -1) l = 0;
        if (r == -1) r = arr.Length;
        while (l < r)
        {
            int x = (l + r) / 2;
            if (comp(arr[x]) < 0) l = x + 1;
            else r = x;
        }
        return l;
    }
    public static int LowerBound<T>(in List<T> list, Func<T, int> comp, int l = -1, int r = -1)
    {
        if (list.Count == 0) return -1;
        if (l == -1) l = 0;
        if (r == -1) r = list.Count;
        while (l < r)
        {
            int x = (l + r) / 2;
            if (comp(list[x]) < 0) l = x + 1;
            else r = x;
        }
        return l;
    }
}

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; } }
    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++];
    }
    public char Char()
    {
        byte b = 0;
        do b = read();
        while (b < 33 || 126 < b);
        return (char)b;
    }
    public string Line()
    {
        var sb = new StringBuilder();
        for (var b = Char(); b != 10 && !isEof; b = (char)read()) sb.Append(b);
        return sb.ToString();
    }
    public string Scan()
    {
        var sb = new StringBuilder();
        for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
        return sb.ToString();
    }
    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';
        }
    }
    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';
        }
    }
    public double Double() { return double.Parse(Scan()); }
}

struct ModInt
{
    public static long MOD = 1000000007;
    public long Val { get; private set; }
    public ModInt(long v) { Val = SafeMod(v, MOD); }
    public override string ToString() { return Val.ToString(); }
    public override bool Equals(object obj) => obj is ModInt other && this.Equals(other);
    public bool Equals(ModInt x) => Val == x.Val;
    public override int GetHashCode() => Val.GetHashCode();
    public static bool operator ==(ModInt a, ModInt b) { return a.Val == b.Val; }
    public static bool operator !=(ModInt a, ModInt b) { return a.Val != b.Val; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator ModInt(long n) => new ModInt(SafeMod(n, MOD));
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt a, ModInt b)
    {
        long r = a.Val + b.Val;
        return new ModInt(r < MOD ? r : r - MOD);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a, ModInt b)
    {
        long r = a.Val - b.Val;
        return new ModInt(r < 0 ? r + MOD : r);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a) => new ModInt(a.Val == 0 ? 0 : MOD - a.Val);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt a, ModInt b) => new ModInt(a.Val * b.Val % MOD);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator /(ModInt a, ModInt b) => a * b.Inv();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ModInt Pow(long n)
    {
        long t = Val, r = 1;
        while (n > 0)
        {
            if ((n & 1) == 1) r = r * t % MOD;
            t = t * t % MOD;
            n >>= 1;
        }
        return new ModInt(r);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ModInt Inv() => Gcd(Val, MOD).x;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private static (long x, long y, long g) Gcd(long a, long b)
    {

        if (b == 0) return a >= 0 ? (1, 0, a) : (-1, 0, -a);
        long c = a % b;
        if (c < 0) c += b;
        var r = Gcd(b, c);
        long x = SafeMod(r.y, b);
        long g = r.g;
        long y = (g - a * x) / b;
        return (x, y, g);
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private static long SafeMod(long x, long m)
    {
        long r = x % m;
        return r < 0 ? r + m : r;
    }
}

class ModFact
{
    ModInt[] fact;
    ModInt[] factinv;
    ModInt[] inv;
    public ModFact(long n)
    {
        fact = new ModInt[n + 1];
        factinv = new ModInt[n + 1];
        inv = new ModInt[n + 1];
        fact[0] = 1;
        for (long i = 0; i < n; i++) fact[i + 1] = fact[i] * (i + 1);
        factinv[n] = fact[n].Inv();
        for (long i = n; i > 0; i--) factinv[i - 1] = factinv[i] * i;
        for (long i = 1; i <= n; i++) inv[i] = fact[i - 1] * factinv[i];
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ModInt Fact(long n) => fact[n];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ModInt FactInv(long n) => factinv[n];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ModInt Inv(long n)
    {
        if (n == 0) throw new DivideByZeroException();
        return inv[n];
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ModInt Binom(long n, long k)
    {
        if (n < 0) return 0;
        if (n == 0) return k == 0 ? 1 : 0;
        return 0 <= k && k <= n ? fact[n] * factinv[k] * factinv[n - k] : 0;
    }
}