#1147116 (C#) No.3443 Sum of (Tree Distances)^K 1

• 問題: No.3443 Sum of (Tree Distances)^K 1
• ユーザー: tobisatis
• 提出日時: 2026-02-06 23:15:50
• 言語: C# (.NET 10.0.101)
• 結果: AC
• 実行時間: 360 ms / 2,000 ms
• コード長: 10,225 bytes
• コンパイル時間: 21,109 ms
• コンパイル使用メモリ: 171,748 KB
• 実行使用メモリ: 207,236 KB
• 最終ジャッジ日時: 2026-02-06 23:16:23
• 合計ジャッジ時間: 25,511 ms
• ジャッジサーバーID （参考情報）: judge1 / judge5

ファイルパターン	結果
sample	AC * 3
other	AC * 47

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 (174 ミリ秒)。
  main -> /home/judge/data/code/bin/Release/net10.0/main.dll
  main -> /home/judge/data/code/bin/Release/net10.0/publish/

ソースコード

#nullable enable

#region
var (_input, _iter) = (Array.Empty<string>(), 0);
T I<T>() where T : IParsable<T>
{
    while (_iter >= _input.Length) (_input, _iter) = (Console.ReadLine()!.Split(' '), 0);
    return T.Parse(_input[_iter++], null);
}
#endregion

var n = I<int>();
var k = I<int>();

FPSNTT.MaxLength = n + 1;
ModInt m = n;
var fiz = new FPSNTT();
for (var i = 0; i <= n; i++) fiz[i] = (-i).Factorial();
var g = new FPSNTT();
for (var i = 2; i <= n; i++) g[i] = i * m.Power(n - i - 1) * ((ModInt)i - 1).Power(k);
var f = g * fiz;
var ans = new ModInt[n + 1];
for (var i = 1; i <= n; i++) ans[i] = f[i] * i.Factorial() / 2;
for (var i = n; i > 0; i--) ans[i] -= ans[i - 1];
Console.WriteLine(string.Join(Environment.NewLine, ans[1..]));

readonly record struct ModInt
{
    public const int Mod = 998244353;
    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() => V == 0 ? throw new DivideByZeroException() : Power(V, Mod - 2, Mod);
    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 ? MultiplicativeInverse().Power(-p) : Power(V, (ulong)p, Mod);

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

static class FactorialExtensions
{
    public static ModInt Factorial(this int value)
    {
        Extend(value);
        return value < 0 ? _inv[-value] : _fac[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 ModInt[] _fac = new ModInt[]{ 1 };
    static 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 <<= 1;
        var fac = new ModInt[l];
        var inv = new ModInt[l];
        fac[0] = 1;
        for (var i = 1; i < fac.Length; i++) fac[i] = fac[i - 1] * i;
        inv[l - 1] = fac[l - 1].Power(-1);
        for (var i = inv.Length - 1; i > 0; i--) inv[i - 1] = inv[i] * i;
        (_fac, _inv) = (fac, inv);
    }
}

partial class FPSNTT
{
    public static int MaxLength = -4;
    public const int Mod = (1 << 23) * 119 + 1;
    long[] _data = new[]{ 0L };
    int _length = 1;

    public FPSNTT() { }
    public static FPSNTT From(ReadOnlySpan<long> a)
    {
        var res = new FPSNTT();
        for (var i = 0; i < a.Length; i++) res[i] = a[i];
        return res;
    }

    public long this[int i]
    {
        get => i < _length ? _data[i] : 0;
        set
        {
            Resize(i);
            _data[i] = Rem(value);
        }
    }
    public long[] Slice(int start, int length)
    {
        var res = new long[length];
        for (var i = 0; i < length; i++) res[i] = this[start + i];
        return res;
    }

    public static FPSNTT operator *(FPSNTT f, long k)
    {
        k = Rem(k);
        var a = new long[f._data.Length];
        for (var i = 0; i < a.Length; i++) a[i] = f[i] * k % Mod;
        return new(a);
    }
    public static FPSNTT operator /(FPSNTT f, long k) => f * Pow(k, -1);

    public static FPSNTT AdditiveIdentity => new(new[]{ 0L });
    public static FPSNTT operator +(FPSNTT l, FPSNTT r)
    {
        if (l._length < r._length) (l, r) = (r, l);
        var (llen, rlen) = (l._length, r._length);
        var a = new long[l._data.Length];
        for (var i = 0; i < llen; i++) a[i] += l[i];
        for (var i = 0; i < rlen; i++) a[i] = (a[i] + r[i]) % Mod;
        return new(a);
    }
    public FPSNTT AdditiveInverse() => this * -1;
    public static FPSNTT operator -(FPSNTT l, FPSNTT r) => l + r * -1;

    public static FPSNTT MultiplicativeIdentity => new(new[]{ 1L });
    public static FPSNTT operator *(FPSNTT f, FPSNTT g) => new(Mul(f.ToSpan(), g.ToSpan()), f._length + g._length - 1);
    public FPSNTT MultiplicativeInverse()
    {
        if (_data[0] == 0) throw new Exception("the constant term must not be zero");
        return new(Inv(ToSpan(), MaxLength));
    }
    public static FPSNTT operator /(FPSNTT l, FPSNTT r) => l * r.MultiplicativeInverse();

    ReadOnlySpan<long> ToSpan() => _data.AsSpan()[.._length];
    void Resize(int idx)
    {
        _length = Math.Max(_length, idx + 1);
        var len = _data.Length;
        if (idx < len) return;
        if (idx >= MaxLength) throw new IndexOutOfRangeException();
        var len2 = len;
        while (idx >= len2) len2 <<= 1;
        var (data, data2) = (_data, new long[len2]);
        for (var i = 0; i < len; i++) data2[i] = data[i];
        _data = data2;
    }

    static long[] Expanded(ReadOnlySpan<long> data, int level)
    {
        var res = new long[1 << level];
        data.CopyTo(res);
        return res;
    }

    FPSNTT(long[] data, int length) { _data = data; _length = Math.Min(length, MaxLength); }
    FPSNTT(long[] data) { _data = data; _length = Math.Min(data.Length, MaxLength); }
    static long Rem(long v)
    {
        var res = v % Mod;
        return res < 0 ? res + Mod : res;
    }
    static long Pow(long n, long m)
    {
        if (m < 0) m = (m % (Mod - 1)) + Mod - 1;
        var (res, k) = (1L, n);
        while (m > 0)
        {
            if ((m & 1) > 0) res = res * k % Mod;
            k = k * k % Mod;
            m >>= 1;
        }
        return res;
    }

    static readonly long[] _r1, _r2;

    static FPSNTT()
    {
        var r1 = new long[23 + 1];
        var r2 = new long[23 + 1];
        var u = Pow(3, 119);
        (r1[23], r2[23]) = (u, Pow(u, -1));
        for (var i = 23; i > 0; i--)
        {
            r1[i - 1] = r1[i] * r1[i] % Mod;
            r2[i - 1] = r2[i] * r2[i] % Mod;
        }
        (_r1, _r2) = (r1, r2);
    }

    static void FastModuloTransform(Span<long> f, int level, bool reverse)
    {
        var n = f.Length;
        if (n < 2) return;
        var b = new int[n];
        for (int p = 1, d = n >> 1; p < n; p <<= 1, d >>= 1) for (var k = 0; k < p; ++k) b[k | p] = b[k] | d;
        for (var i = 0; i < n; i++)
        {
            var j = b[i];
            if (i < j) (f[i], f[j]) = (f[j], f[i]);
        }
        var rotations = reverse ? _r1 : _r2;
        for (var k = 1; k <= level; k++)
        {
            var l = 1 << k;
            var h = l >> 1;
            var root = rotations[k];
            for (var i = 0; i < n; i += l)
            {
                var rotation = 1L;
                for (var j = 0; j < h; j++)
                {
                    var (ui, vi) = (i + j, i + j + h);
                    var (u, v) = (f[ui], f[vi] * rotation % Mod);
                    (f[ui], f[vi]) = ((u + v) % Mod, (u - v + Mod) % Mod);
                    rotation = rotation * root % Mod;
                }
            }
        }
    }

    static long[] Mul(ReadOnlySpan<long> f, ReadOnlySpan<long> g, int len = -1)
    {
        if (len < 0) len = f.Length + g.Length - 1;
        var (n, level) = (1, 0);
        while (n < len) (n, level) = (n << 1, level + 1);
        var ft = Expanded(f, level);
        var gt = Expanded(g, level);
        FastModuloTransform(ft, level, false);
        FastModuloTransform(gt, level, false);
        for (var i = 0; i < n; i++) ft[i] = ft[i] * gt[i] % Mod;
        FastModuloTransform(ft, level, true);
        var nInverse = Pow(n, -1);
        for (var i = 0; i < len; i++) ft[i] = ft[i] * nInverse % Mod;
        for (var i = len; i < n; i++) ft[i] = 0;
        return ft;
    }

    static long[] InvStep(ReadOnlySpan<long> f, ReadOnlySpan<long> g)
    {
        var l1 = g.Length;
        var l2 = l1 << 1;
        var flen = Math.Min(f.Length, l2);
        var h = Mul(f[..flen], g, l2);
        h.AsSpan()[..l1].Clear();
        h = Mul(h, g, l2);
        for (var i = 0; i < l1; i++) h[i] = g[i];
        for (var i = l1; i < l2; i++) h[i] = (Mod - h[i]) % Mod;
        return h;
    }

    static long[] Inv(ReadOnlySpan<long> f, int tl)
    {
        var g = new[]{ Pow(f[0], -1) };
        if (f.Length == 1) return g;
        while (g.Length < tl) g = InvStep(f, g);
        return g;
    }
}