#589615 (C#(csc)) No.1307 Rotate and Accumulate

提出ソース

結果

問題	No.1307 Rotate and Accumulate
ユーザー	takytank
提出日時	2020-12-05 16:25:10
言語	C#(csc) (csc 3.9.0)
結果	AC
実行時間	1,128 ms / 5,000 ms
コード長	32,621 bytes
コンパイル時間	5,178 ms
コンパイル使用メモリ	121,472 KB
実行使用メモリ	36,736 KB
最終ジャッジ日時	2024-09-15 17:58:46
合計ジャッジ時間	15,802 ms
ジャッジサーバーID （参考情報）	judge5 / judge4

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	37 ms 18,048 KB
testcase_01	AC	37 ms 17,920 KB
testcase_02	AC	36 ms 18,176 KB
testcase_03	AC	36 ms 17,920 KB
testcase_04	AC	38 ms 18,048 KB
testcase_05	AC	36 ms 17,920 KB
testcase_06	AC	37 ms 18,304 KB
testcase_07	AC	36 ms 18,176 KB
testcase_08	AC	1,089 ms 34,560 KB
testcase_09	AC	1,092 ms 34,944 KB
testcase_10	AC	558 ms 27,904 KB
testcase_11	AC	563 ms 30,592 KB
testcase_12	AC	560 ms 28,160 KB
testcase_13	AC	96 ms 18,560 KB
testcase_14	AC	286 ms 22,656 KB
testcase_15	AC	1,128 ms 36,736 KB
testcase_16	AC	1,125 ms 36,608 KB
testcase_17	AC	1,125 ms 36,608 KB
testcase_18	AC	911 ms 36,608 KB
testcase_19	AC	971 ms 36,608 KB
testcase_20	AC	919 ms 36,480 KB
testcase_21	AC	37 ms 18,048 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

Microsoft (R) Visual C# Compiler version 3.9.0-6.21124.20 (db94f4cc)
Copyright (C) Microsoft Corporation. All rights reserved.

ソースコード

raw source code

using System;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Text;

namespace YukiCoder
{
	class Program
	{
		static void Main()
		{
			using var cin = new Scanner();
			var (n, q) = cin.Int2();
			var a = cin.ArrayLong(n);
			var b = new long[n + 2];
			for (int i = 0; i < q; i++) {
				int r = cin.Int();
				b[(n - r) % n]++;
			}

			var conv = Convolution.Convolve(a, b);
			var ret = new long[n];
			for (int i = 0; i < n; i++) {
				ret[i] += conv[i];
				ret[i] += conv[i + n];
			}

			Console.WriteLine(ret.Join(" "));
		}
	}

	public static class Convolution
	{
		public static long[] Convolve(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 = FftMod1.MOD;
				const ulong Mod2 = FftMod2.MOD;
				const ulong Mod3 = FftMod3.MOD;
				const ulong M2M3 = Mod2 * Mod3;
				const ulong M1M3 = Mod1 * Mod3;
				const ulong M1M2 = Mod1 * Mod2;
				const ulong M1M2M3 = Mod1 * Mod2 * Mod3;

				ulong i1 = (ulong)InverseGCD((long)M2M3, (long)Mod1).x;
				ulong i2 = (ulong)InverseGCD((long)M1M3, (long)Mod2).x;
				ulong i3 = (ulong)InverseGCD((long)M1M2, (long)Mod3).x;

				var c1 = Convolve<FftMod1>(a, b);
				var c2 = Convolve<FftMod2>(a, b);
				var c3 = Convolve<FftMod3>(a, b);

				var c = new long[n + m - 1];

				Span<ulong> offset = stackalloc ulong[] { 0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3 };

				for (int i = 0; i < c.Length; i++) {
					ulong x = 0;
					x += (c1[i] * i1) % Mod1 * M2M3;
					x += (c2[i] * i2) % Mod2 * M1M3;
					x += (c3[i] * i3) % Mod3 * M1M2;

					long diff = (long)c1[i] - SafeMod((long)x, (long)Mod1);
					if (diff < 0) {
						diff += (long)Mod1;
					}

					x -= offset[(int)(diff % offset.Length)];
					c[i] = (long)x;
				}

				return c;
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private static ulong[] Convolve<TMod>(ReadOnlySpan<long> a, ReadOnlySpan<long> b)
				where TMod : struct, IFftMod
		{
			int z = 1 << CeilPow2(a.Length + b.Length - 1);

			var aTemp = new FftModInt<TMod>[z];
			for (int i = 0; i < a.Length; i++) {
				aTemp[i] = new FftModInt<TMod>(a[i]);
			}

			var bTemp = new FftModInt<TMod>[z];
			for (int i = 0; i < b.Length; i++) {
				bTemp[i] = new FftModInt<TMod>(b[i]);
			}

			var c = Convolve<TMod>(aTemp, bTemp, a.Length, b.Length, z);
			var result = new ulong[c.Length];
			for (int i = 0; i < result.Length; i++) {
				result[i] = (ulong)c[i].Value;
			}

			return result;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private static Span<FftModInt<TMod>> Convolve<TMod>(Span<FftModInt<TMod>> a, Span<FftModInt<TMod>> b, int n, int m, int z)
			where TMod : struct, IFftMod
		{
			FftModInt<TMod>.Butterfly(a);
			FftModInt<TMod>.Butterfly(b);

			for (int i = 0; i < a.Length; i++) {
				a[i] *= b[i];
			}

			FftModInt<TMod>.ButterflyInv(a);
			var result = a[0..(n + m - 1)];
			var iz = new FftModInt<TMod>(z).Inv();
			foreach (ref var r in result) {
				r *= iz;
			}

			return result;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private static long SafeMod(long x, long m)
		{
			x %= m;
			if (x < 0) {
				x += m;
			}

			return x;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private static (long g, long x) InverseGCD(long a, long b)
		{
			a = SafeMod(a, b);
			if (a == 0) {
				return (b, 0);
			}

			long s = b;
			long t = a;
			long m0 = 0;
			long 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(MethodImplOptions.AggressiveInlining)]
		private static int CeilPow2(int n)
		{
			var un = (uint)n;
			if (un <= 1) {
				return 0;
			}

			int ret = 0;
			int pow = 1;
			while (n > pow) {
				++ret;
				pow *= 2;
			}

			return ret;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private static int BitScanForward(uint n)
		{
			for (int i = 0; i < 32; i++) {
				if (((1 << i) & n) != 0) {
					return i;
				}
			}

			return -1;
		}

		private interface IFftMod
		{
			uint Mod { get; }
			int PrimitiveRoot { get; }
			bool IsPrime { get; }
		}

		private readonly struct FftMod1 : IFftMod
		{
			public const uint MOD = 754974721;
			public uint Mod => MOD;
			public int PrimitiveRoot => 11;
			public bool IsPrime => true;
		}

		private readonly struct FftMod2 : IFftMod
		{
			public const uint MOD = 167772161;
			public uint Mod => MOD;
			public int PrimitiveRoot => 3;
			public bool IsPrime => true;
		}

		private readonly struct FftMod3 : IFftMod
		{
			public const uint MOD = 469762049;
			public uint Mod => MOD;
			public int PrimitiveRoot => 3;
			public bool IsPrime => true;
		}

		private readonly struct FftModInt<T> where T : struct, IFftMod
		{
			private readonly uint v_;
			public int Value => (int)v_;
			public static int Mod => (int)default(T).Mod;

			private static FftModInt<T>[] sumE_ = null;
			private static FftModInt<T>[] sumIE_ = null;

			public static FftModInt<T> Raw(int v)
			{
				var u = unchecked((uint)v);
				return new FftModInt<T>(u);
			}

			public static void Butterfly(Span<FftModInt<T>> a)
			{
				if (sumE_ is null) {
					sumE_ = CalcurateSumE();
				}

				var n = a.Length;
				var h = CeilPow2(n);

				for (int ph = 1; ph <= h; ph++) {
					int w = 1 << (ph - 1);
					int p = 1 << (h - ph);
					var now = Raw(1);
					for (int s = 0; s < w; s++) {
						int offset = s << (h - ph + 1);
						for (int i = 0; i < p; i++) {
							var l = a[i + offset];
							var r = a[i + offset + p] * now;
							a[i + offset] = l + r;
							a[i + offset + p] = l - r;
						}

						now *= sumE_[BitScanForward(~(uint)s)];
					}
				}
			}

			public static void ButterflyInv(Span<FftModInt<T>> a)
			{
				if (sumIE_ is null) {
					sumIE_ = CalcurateSumIE();
				}

				var n = a.Length;
				var h = CeilPow2(n);

				for (int ph = h; ph >= 1; ph--) {
					int w = 1 << (ph - 1);
					int p = 1 << (h - ph);
					var iNow = Raw(1);
					for (int s = 0; s < w; s++) {
						int offset = s << (h - ph + 1);
						for (int i = 0; i < p; i++) {
							var l = a[i + offset];
							var r = a[i + offset + p];
							a[i + offset] = l + r;
							a[i + offset + p] = Raw(
								unchecked((int)((ulong)(default(T).Mod + l.Value - r.Value) * (ulong)iNow.Value % default(T).Mod)));
						}

						iNow *= sumIE_[BitScanForward(~(uint)s)];
					}
				}
			}

			public FftModInt(long v) : this(Round(v)) { }
			private FftModInt(uint v) => v_ = v;
			private static uint Round(long v)
			{
				var x = v % default(T).Mod;
				if (x < 0) {
					x += default(T).Mod;
				}
				return (uint)x;
			}

			public static FftModInt<T> operator ++(FftModInt<T> value)
			{
				var v = value.v_ + 1;
				if (v == default(T).Mod) {
					v = 0;
				}
				return new FftModInt<T>(v);
			}

			public static FftModInt<T> operator --(FftModInt<T> value)
			{
				var v = value.v_;
				if (v == 0) {
					v = default(T).Mod;
				}
				return new FftModInt<T>(v - 1);
			}

			public static FftModInt<T> operator +(FftModInt<T> lhs, FftModInt<T> rhs)
			{
				var v = lhs.v_ + rhs.v_;
				if (v >= default(T).Mod) {
					v -= default(T).Mod;
				}
				return new FftModInt<T>(v);
			}

			public static FftModInt<T> operator -(FftModInt<T> lhs, FftModInt<T> rhs)
			{
				unchecked {
					var v = lhs.v_ - rhs.v_;
					if (v >= default(T).Mod) {
						v += default(T).Mod;
					}
					return new FftModInt<T>(v);
				}
			}

			public static FftModInt<T> operator *(FftModInt<T> lhs, FftModInt<T> rhs)
			{
				return new FftModInt<T>((uint)((ulong)lhs.v_ * rhs.v_ % default(T).Mod));
			}

			public static FftModInt<T> operator /(FftModInt<T> lhs, FftModInt<T> rhs) => lhs * rhs.Inv();

			public static FftModInt<T> operator +(FftModInt<T> value) => value;
			public static FftModInt<T> operator -(FftModInt<T> value) => new FftModInt<T>() - value;
			public static bool operator ==(FftModInt<T> lhs, FftModInt<T> rhs) => lhs.v_ == rhs.v_;
			public static bool operator !=(FftModInt<T> lhs, FftModInt<T> rhs) => lhs.v_ != rhs.v_;
			public static implicit operator FftModInt<T>(int value) => new FftModInt<T>(value);
			public static implicit operator FftModInt<T>(long value) => new FftModInt<T>(value);

			public FftModInt<T> Pow(long n)
			{
				var x = this;
				var r = new FftModInt<T>(1u);

				while (n > 0) {
					if ((n & 1) > 0) {
						r *= x;
					}
					x *= x;
					n >>= 1;
				}

				return r;
			}

			public FftModInt<T> Inv()
			{
				if (default(T).IsPrime) {
					return Pow(default(T).Mod - 2);
				} else {
					var (_, x) = InverseGCD(v_, default(T).Mod);
					return new FftModInt<T>(x);
				}
			}

			public override string ToString() => v_.ToString();
			public override bool Equals(object obj) => obj is FftModInt<T> value && this == value;
			public override int GetHashCode() => v_.GetHashCode();

			private static FftModInt<T>[] CalcurateSumE()
			{
				int g = default(T).PrimitiveRoot;
				int cnt2 = BitScanForward(default(T).Mod - 1);
				var e = new FftModInt<T>(g).Pow((default(T).Mod - 1) >> cnt2);
				var ie = e.Inv();

				var sumE = new FftModInt<T>[cnt2 - 2];

				Span<FftModInt<T>> es = stackalloc FftModInt<T>[cnt2 - 1];
				Span<FftModInt<T>> ies = stackalloc FftModInt<T>[cnt2 - 1];

				for (int i = es.Length - 1; i >= 0; i--) {
					es[i] = e;
					ies[i] = ie;
					e *= e;
					ie *= ie;
				}

				var now = Raw(1);
				for (int i = 0; i < sumE.Length; i++) {
					sumE[i] = es[i] * now;
					now *= ies[i];
				}

				return sumE;
			}

			private static FftModInt<T>[] CalcurateSumIE()
			{
				int g = default(T).PrimitiveRoot;
				int cnt2 = BitScanForward(default(T).Mod - 1);
				var e = new FftModInt<T>(g).Pow((default(T).Mod - 1) >> cnt2);
				var ie = e.Inv();

				var sumIE = new FftModInt<T>[cnt2 - 2];

				Span<FftModInt<T>> es = stackalloc FftModInt<T>[cnt2 - 1];
				Span<FftModInt<T>> ies = stackalloc FftModInt<T>[cnt2 - 1];

				for (int i = es.Length - 1; i >= 0; i--) {
					es[i] = e;
					ies[i] = ie;
					e *= e;
					ie *= ie;
				}

				var now = Raw(1);
				for (int i = 0; i < sumIE.Length; i++) {
					sumIE[i] = ies[i] * now;
					now *= es[i];
				}

				return sumIE;
			}
		}
	}

	public struct BitFlag
	{
		public static BitFlag Begin() => 0;
		public static BitFlag End(int bitCount) => 1 << bitCount;
		public static BitFlag FromBit(int bitNumber) => 1 << bitNumber;

		private readonly int flags_;
		public int Flag => flags_;
		public bool this[int bitNumber] => (flags_ & (1 << bitNumber)) != 0;
		public BitFlag(int flags) { flags_ = flags; }

		public bool Has(BitFlag target) => (flags_ & target.flags_) == target.flags_;
		public bool Has(int target) => (flags_ & target) == target;
		public bool HasBit(int bitNumber) => (flags_ & (1 << bitNumber)) != 0;
		public BitFlag OrBit(int bitNumber) => (flags_ | (1 << bitNumber));
		public BitFlag AndBit(int bitNumber) => (flags_ & (1 << bitNumber));
		public BitFlag XorBit(int bitNumber) => (flags_ ^ (1 << bitNumber));

		public static BitFlag operator ++(BitFlag src) => new BitFlag(src.flags_ + 1);
		public static BitFlag operator --(BitFlag src) => new BitFlag(src.flags_ - 1);
		public static BitFlag operator |(BitFlag lhs, BitFlag rhs)
			=> new BitFlag(lhs.flags_ | rhs.flags_);
		public static BitFlag operator |(BitFlag lhs, int rhs)
			=> new BitFlag(lhs.flags_ | rhs);
		public static BitFlag operator |(int lhs, BitFlag rhs)
			=> new BitFlag(lhs | rhs.flags_);
		public static BitFlag operator &(BitFlag lhs, BitFlag rhs)
			=> new BitFlag(lhs.flags_ & rhs.flags_);
		public static BitFlag operator &(BitFlag lhs, int rhs)
			=> new BitFlag(lhs.flags_ & rhs);
		public static BitFlag operator &(int lhs, BitFlag rhs)
			=> new BitFlag(lhs & rhs.flags_);

		public static bool operator <(BitFlag lhs, BitFlag rhs) => lhs.flags_ < rhs.flags_;
		public static bool operator <(BitFlag lhs, int rhs) => lhs.flags_ < rhs;
		public static bool operator <(int lhs, BitFlag rhs) => lhs < rhs.flags_;
		public static bool operator >(BitFlag lhs, BitFlag rhs) => lhs.flags_ > rhs.flags_;
		public static bool operator >(BitFlag lhs, int rhs) => lhs.flags_ > rhs;
		public static bool operator >(int lhs, BitFlag rhs) => lhs > rhs.flags_;
		public static bool operator <=(BitFlag lhs, BitFlag rhs) => lhs.flags_ <= rhs.flags_;
		public static bool operator <=(BitFlag lhs, int rhs) => lhs.flags_ <= rhs;
		public static bool operator <=(int lhs, BitFlag rhs) => lhs <= rhs.flags_;
		public static bool operator >=(BitFlag lhs, BitFlag rhs) => lhs.flags_ >= rhs.flags_;
		public static bool operator >=(BitFlag lhs, int rhs) => lhs.flags_ >= rhs;
		public static bool operator >=(int lhs, BitFlag rhs) => lhs >= rhs.flags_;

		public static implicit operator BitFlag(int t) => new BitFlag(t);
		public static implicit operator int(BitFlag t) => t.flags_;

		public override string ToString() => $"{Convert.ToString(flags_, 2).PadLeft(32, '0')} ({flags_})";

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void ForEachSubBits(Action<BitFlag> action)
		{
			for (BitFlag sub = flags_; sub >= 0; --sub) {
				sub &= flags_;
				action(sub);
			}
		}
	}

	public class HashMap<TKey, TValue> : Dictionary<TKey, TValue>
	{
		private readonly Func<TKey, TValue> initialzier_;
		public HashMap(Func<TKey, TValue> initialzier)
			: base()
		{
			initialzier_ = initialzier;
		}

		public HashMap(Func<TKey, TValue> initialzier, int capacity)
			: base(capacity)
		{
			initialzier_ = initialzier;
		}

		new public TValue this[TKey key]
		{
			get
			{
				if (TryGetValue(key, out TValue value)) {
					return value;
				} else {
					var init = initialzier_(key);
					base[key] = init;
					return init;
				}
			}

			set { base[key] = value; }
		}

		public HashMap<TKey, TValue> Merge(
			HashMap<TKey, TValue> src,
			Func<TValue, TValue, TValue> mergeValues)
		{
			foreach (var key in src.Keys) {
				this[key] = mergeValues(this[key], src[key]);
			}

			return this;
		}
	}

	public struct ModInt
	{
		//public const long P = 1000000007;
		public const long P = 998244353;
		public const long ROOT = 3;

		// (924844033, 5)
		// (998244353, 3)
		// (1012924417, 5)
		// (167772161, 3)
		// (469762049, 3)
		// (1224736769, 3)

		private long value_;

		public ModInt(long value)
			=> value_ = value;
		public ModInt(long value, bool mods)
		{
			if (mods) {
				value %= P;
				if (value < 0) {
					value += P;
				}
			}

			value_ = value;
		}

		public static ModInt operator +(ModInt lhs, ModInt rhs)
		{
			lhs.value_ = (lhs.value_ + rhs.value_) % P;
			return lhs;
		}
		public static ModInt operator +(long lhs, ModInt rhs)
		{
			rhs.value_ = (lhs + rhs.value_) % P;
			return rhs;
		}
		public static ModInt operator +(ModInt lhs, long rhs)
		{
			lhs.value_ = (lhs.value_ + rhs) % P;
			return lhs;
		}

		public static ModInt operator -(ModInt lhs, ModInt rhs)
		{
			lhs.value_ = (P + lhs.value_ - rhs.value_) % P;
			return lhs;
		}
		public static ModInt operator -(long lhs, ModInt rhs)
		{
			rhs.value_ = (P + lhs - rhs.value_) % P;
			return rhs;
		}
		public static ModInt operator -(ModInt lhs, long rhs)
		{
			lhs.value_ = (P + lhs.value_ - rhs) % P;
			return lhs;
		}

		public static ModInt operator *(ModInt lhs, ModInt rhs)
		{
			lhs.value_ = lhs.value_ * rhs.value_ % P;
			return lhs;
		}
		public static ModInt operator *(long lhs, ModInt rhs)
		{
			rhs.value_ = lhs * rhs.value_ % P;
			return rhs;
		}
		public static ModInt operator *(ModInt lhs, long rhs)
		{
			lhs.value_ = lhs.value_ * rhs % P;
			return lhs;
		}

		public static ModInt operator /(ModInt lhs, ModInt rhs)
		{
			long exp = P - 2;
			while (exp > 0) {
				if (exp % 2 > 0) {
					lhs *= rhs;
				}

				rhs *= rhs;
				exp /= 2;
			}

			return lhs;
		}

		public static implicit operator ModInt(long n) => new ModInt(n, true);

		public static ModInt Inverse(ModInt value) => Pow(value, P - 2);
		public static ModInt Pow(ModInt value, long k) => Pow(value.value_, k);
		public static ModInt Pow(long value, long k)
		{
			long ret = 1;
			for (k %= P - 1; k > 0; k >>= 1, value = value * value % P) {
				if ((k & 1) == 1) {
					ret = ret * value % P;
				}
			}
			return new ModInt(ret);
		}


		public static Span<ModInt> NumberTheoreticTransform(
			Span<int> values, bool inverses = false)
		{
			var mods = new ModInt[values.Length];
			for (int i = 0; i < mods.Length; i++) {
				mods[i] = new ModInt(values[i]);
			}

			return NumberTheoreticTransform(mods, inverses);
		}

		public static Span<ModInt> NumberTheoreticTransform(
			Span<long> values, bool inverses = false)
		{
			var mods = new ModInt[values.Length];
			for (int i = 0; i < mods.Length; i++) {
				mods[i] = new ModInt(values[i]);
			}

			return NumberTheoreticTransform(mods, inverses);
		}

		public static Span<ModInt> NumberTheoreticTransform(
			Span<ModInt> a, bool inverses = false)
		{
			int n = a.Length;
			if (n == 1) {
				return a;
			}

			var b = new ModInt[n].AsSpan();
			int r = inverses
				? (int)(P - 1 - (P - 1) / n)
				: (int)((P - 1) / n);
			ModInt s = Pow(ROOT, r);
			var kp = new ModInt[n / 2 + 1];
			kp.AsSpan().Fill(1);

			for (int i = 0; i < n / 2; ++i) {
				kp[i + 1] = kp[i] * s;
			}

			int l = n / 2;
			for (int i = 1; i < n; i <<= 1, l >>= 1) {
				r = 0;
				for (int j = 0; j < l; ++j, r += i) {
					s = kp[i * j];
					for (int k = 0; k < i; ++k) {
						var p = a[k + r];
						var q = a[k + r + n / 2];
						b[k + 2 * r] = p + q;
						b[k + 2 * r + i] = (p - q) * s;
					}
				}

				var temp = a;
				a = b;
				b = temp;
			}

			if (inverses) {
				s = Inverse(n);
				for (int i = 0; i < n; i++) {
					a[i] = a[i] * s;
				}
			}

			return a;
		}

		public static ModInt[,] NumberTheoreticTransform2D(ModInt[,] a, bool inverses = false)
		{
			int h = a.GetLength(0);
			int w = a.GetLength(1);
			if (h == 1 && w == 1) {
				return a;
			}

			var b = new ModInt[h, w];

			{
				int n = w;
				int r = inverses
					? (int)(P - 1 - (P - 1) / n)
					: (int)((P - 1) / n);
				ModInt s = Pow(ROOT, r);
				var kp = new ModInt[n / 2 + 1];
				kp.AsSpan().Fill(1);

				for (int i = 0; i < n / 2; ++i) {
					kp[i + 1] = kp[i] * s;
				}

				for (int y = 0; y < h; y++) {
					int l = n / 2;
					for (int i = 1; i < n; i <<= 1, l >>= 1) {
						r = 0;
						for (int j = 0; j < l; ++j, r += i) {
							s = kp[i * j];
							for (int k = 0; k < i; ++k) {
								var p = a[y, k + r];
								var q = a[y, k + r + n / 2];
								b[y, k + 2 * r] = p + q;
								b[y, k + 2 * r + i] = (p - q) * s;
							}
						}

						var temp = a;
						a = b;
						b = temp;
					}

					if (inverses) {
						s = Inverse(n);
						for (int i = 0; i < n; i++) {
							a[y, i] = a[y, i] * s;
						}
					}
				}
			}

			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					b[h, w] = 0;
				}
			}

			{
				int n = h;
				int r = inverses
					? (int)(P - 1 - (P - 1) / n)
					: (int)((P - 1) / n);
				ModInt s = Pow(ROOT, r);
				var kp = new ModInt[n / 2 + 1];
				kp.AsSpan().Fill(1);

				for (int i = 0; i < n / 2; ++i) {
					kp[i + 1] = kp[i] * s;
				}

				for (int x = 0; x < w; x++) {
					int l = n / 2;
					for (int i = 1; i < n; i <<= 1, l >>= 1) {
						r = 0;
						for (int j = 0; j < l; ++j, r += i) {
							s = kp[i * j];
							for (int k = 0; k < i; ++k) {
								var p = a[k + r, x];
								var q = a[k + r + n / 2, x];
								b[k + 2 * r, x] = p + q;
								b[k + 2 * r + i, x] = (p - q) * s;
							}
						}

						var temp = a;
						a = b;
						b = temp;
					}

					if (inverses) {
						s = Inverse(n);
						for (int i = 0; i < n; i++) {
							a[i, x] = a[i, x] * s;
						}
					}
				}
			}

			return a;
		}

		public static Span<ModInt> Convolve(ReadOnlySpan<ModInt> a, ReadOnlySpan<ModInt> b)
		{
			int resultLength = a.Length + b.Length - 1;
			int nttLenght = 1;
			while (nttLenght < resultLength) {
				nttLenght <<= 1;
			}

			var aa = new ModInt[nttLenght];
			a.CopyTo(aa);
			var bb = new ModInt[nttLenght];
			b.CopyTo(bb);

			var fa = NumberTheoreticTransform(aa);
			var fb = NumberTheoreticTransform(bb);
			for (int i = 0; i < nttLenght; i++) {
				fa[i] *= fb[i];
			}

			var convolved = NumberTheoreticTransform(fa, true);
			return convolved.Slice(0, resultLength);
		}

		public long ToLong() => value_;
		public override string ToString() => value_.ToString();
	}

	public static class Helper
	{
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void UpdateMin<T>(this ref T target, T value) where T : struct, IComparable<T>
			=> target = target.CompareTo(value) > 0 ? value : target;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void UpdateMin<T>(this ref T target, T value, Action<T> onUpdated)
			where T : struct, IComparable<T>
		{
			if (target.CompareTo(value) > 0) {
				target = value;
				onUpdated(value);
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void UpdateMax<T>(this ref T target, T value) where T : struct, IComparable<T>
			=> target = target.CompareTo(value) < 0 ? value : target;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void UpdateMax<T>(this ref T target, T value, Action<T> onUpdated)
			where T : struct, IComparable<T>
		{
			if (target.CompareTo(value) < 0) {
				target = value;
				onUpdated(value);
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Array1<T>(int n, T initialValue) where T : struct
			=> new T[n].Fill(initialValue);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Array1<T>(int n, Func<int, T> initializer)
			=> Enumerable.Range(0, n).Select(x => initializer(x)).ToArray();
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Fill<T>(this T[] array, T value)
			where T : struct
		{
			array.AsSpan().Fill(value);
			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,] Array2<T>(int n, int m, T initialValule) where T : struct
			=> new T[n, m].Fill(initialValule);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,] Array2<T>(int n, int m, Func<int, int, T> initializer)
		{
			var array = new T[n, m];
			for (int i = 0; i < n; ++i) {
				for (int j = 0; j < m; ++j) {
					array[i, j] = initializer(i, j);
				}
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,] Fill<T>(this T[,] array, T initialValue)
			where T : struct
		{
			MemoryMarshal.CreateSpan<T>(ref array[0, 0], array.Length).Fill(initialValue);
			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<T> AsSpan<T>(this T[,] array, int i)
			=> MemoryMarshal.CreateSpan<T>(ref array[i, 0], array.GetLength(1));

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,] Array3<T>(int n1, int n2, int n3, T initialValue)
			where T : struct
			=> new T[n1, n2, n3].Fill(initialValue);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,] Fill<T>(this T[,,] array, T initialValue)
			where T : struct
		{
			MemoryMarshal.CreateSpan<T>(ref array[0, 0, 0], array.Length).Fill(initialValue);
			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<T> AsSpan<T>(this T[,,] array, int i, int j)
			=> MemoryMarshal.CreateSpan<T>(ref array[i, j, 0], array.GetLength(2));

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,,] Array4<T>(int n1, int n2, int n3, int n4, T initialValue)
			where T : struct
			=> new T[n1, n2, n3, n4].Fill(initialValue);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[,,,] Fill<T>(this T[,,,] array, T initialValue)
			where T : struct
		{
			MemoryMarshal.CreateSpan<T>(ref array[0, 0, 0, 0], array.Length).Fill(initialValue);
			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<T> AsSpan<T>(this T[,,,] array, int i, int j, int k)
			=> MemoryMarshal.CreateSpan<T>(ref array[i, j, k, 0], array.GetLength(3));

		private static readonly int[] delta4_ = { 1, 0, -1, 0, 1 };
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void DoIn4(int i, int j, int imax, int jmax, Action<int, int> action)
		{
			for (int dn = 0; dn < 4; ++dn) {
				int d4i = i + delta4_[dn];
				int d4j = j + delta4_[dn + 1];
				if ((uint)d4i < (uint)imax && (uint)d4j < (uint)jmax) {
					action(d4i, d4j);
				}
			}
		}

		private static readonly int[] delta8_ = { 1, 0, -1, 0, 1, 1, -1, -1, 1 };
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void DoIn8(int i, int j, int imax, int jmax, Action<int, int> action)
		{
			for (int dn = 0; dn < 8; ++dn) {
				int d8i = i + delta8_[dn];
				int d8j = j + delta8_[dn + 1];
				if ((uint)d8i < (uint)imax && (uint)d8j < (uint)jmax) {
					action(d8i, d8j);
				}
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void ForEachSubBits(int bit, Action<int> action)
		{
			for (int sub = bit; sub >= 0; --sub) {
				sub &= bit;
				action(sub);
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static string Reverse(string src)
		{
			var chars = src.ToCharArray();
			for (int i = 0, j = chars.Length - 1; i < j; ++i, --j) {
				var tmp = chars[i];
				chars[i] = chars[j];
				chars[j] = tmp;
			}

			return new string(chars);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static string Join<T>(this IEnumerable<T> values, string separator = "")
			=> string.Join(separator, values);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static string JoinNL<T>(this IEnumerable<T> values)
			=> string.Join(Environment.NewLine, values);
	}

	public static class Extensions
	{
		public static uint PopCount(uint bits)
		{
			bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555);
			bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333);
			bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f);
			bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff);
			return (bits & 0x0000ffff) + (bits >> 16 & 0x0000ffff);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static int PopCount(this BitFlag bit)
			=> (int)PopCount((uint)bit.Flag);
	}

	public class Scanner : IDisposable
	{
		private const int BUFFER_SIZE = 1024;
		private const int ASCII_CHAR_BEGIN = 33;
		private const int ASCII_CHAR_END = 126;
		private readonly string filePath_;
		private readonly Stream stream_;
		private readonly byte[] buf_ = new byte[BUFFER_SIZE];
		private int length_ = 0;
		private int index_ = 0;
		private bool isEof_ = false;

		public Scanner(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				stream_ = Console.OpenStandardInput();
			} else {
				filePath_ = file;
				stream_ = new FileStream(file, FileMode.Open);
			}

			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) {
				AutoFlush = false
			});
		}

		public void Dispose()
		{
			Console.Out.Flush();
			stream_.Dispose();
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public char Char()
		{
			byte b;
			do {
				b = Read();
			} while (b < ASCII_CHAR_BEGIN || ASCII_CHAR_END < b);

			return (char)b;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public string Next()
		{
			var sb = new StringBuilder();
			for (var b = Char(); b >= ASCII_CHAR_BEGIN && b <= ASCII_CHAR_END; b = (char)Read()) {
				sb.Append(b);
			}

			return sb.ToString();
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public string[] ArrayString(int length)
		{
			var array = new string[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Next();
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public int Int() => (int)Long();
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public int Int(int offset) => Int() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int, int) Int2(int offset = 0)
			=> (Int(offset), Int(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int, int, int) Int3(int offset = 0)
			=> (Int(offset), Int(offset), Int(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (int, int, int, int) Int4(int offset = 0)
			=> (Int(offset), Int(offset), Int(offset), Int(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public int[] ArrayInt(int length, int offset = 0)
		{
			var array = new int[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Int(offset);
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long Long()
		{
			long ret = 0;
			byte b;
			bool 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(MethodImplOptions.AggressiveInlining)]
		public long Long(long offset) => Long() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long, long) Long2(long offset = 0)
			=> (Long(offset), Long(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long, long, long) Long3(long offset = 0)
			=> (Long(offset), Long(offset), Long(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long, long, long, long) Long4(long offset = 0)
			=> (Long(offset), Long(offset), Long(offset), Long(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long[] ArrayLong(int length, long offset = 0)
		{
			var array = new long[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Long(offset);
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public BigInteger Big() => new BigInteger(Long());
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public BigInteger Big(long offset) => Big() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (BigInteger, BigInteger) Big2(long offset = 0)
			=> (Big(offset), Big(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (BigInteger, BigInteger, BigInteger) Big3(long offset = 0)
			=> (Big(offset), Big(offset), Big(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (BigInteger, BigInteger, BigInteger, BigInteger) Big4(long offset = 0)
			=> (Big(offset), Big(offset), Big(offset), Big(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public BigInteger[] ArrayBig(int length, long offset = 0)
		{
			var array = new BigInteger[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Big(offset);
			}

			return array;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public double Double() => double.Parse(Next(), CultureInfo.InvariantCulture);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public double Double(double offset) => Double() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (double, double) Double2(double offset = 0)
			=> (Double(offset), Double(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (double, double, double) Double3(double offset = 0)
			=> (Double(offset), Double(offset), Double(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (double, double, double, double) Double4(double offset = 0)
			=> (Double(offset), Double(offset), Double(offset), Double(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public double[] ArrayDouble(int length, double offset = 0)
		{
			var array = new double[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Double(offset);
			}

			return array;
		}

		private byte Read()
		{
			if (isEof_) {
				throw new EndOfStreamException();
			}

			if (index_ >= length_) {
				index_ = 0;
				if ((length_ = stream_.Read(buf_, 0, BUFFER_SIZE)) <= 0) {
					isEof_ = true;
					return 0;
				}
			}

			return buf_[index_++];
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}

yukicoder

結果

テストケース

コンパイルメッセージ

ソースコード