#648547 (C#(csc)) No.1479 Matrix Eraser

• 問題: No.1479 Matrix Eraser
• ユーザー: takytank
• 提出日時: 2021-04-16 20:54:55
• 言語: C#(csc) (csc 3.9.0)
• 結果: AC
• 実行時間: 466 ms / 3,000 ms
• コード長: 33,369 bytes
• コンパイル時間: 3,039 ms
• コンパイル使用メモリ: 129,188 KB
• 実行使用メモリ: 73,280 KB
• 最終ジャッジ日時: 2024-07-02 23:37:20
• 合計ジャッジ時間: 14,455 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	35 ms; 28,112 KB
testcase_01	AC	36 ms; 28,272 KB
testcase_02	AC	36 ms; 26,328 KB
testcase_03	AC	36 ms; 26,200 KB
testcase_04	AC	36 ms; 26,204 KB
testcase_05	AC	36 ms; 24,500 KB
testcase_06	AC	35 ms; 26,584 KB
testcase_07	AC	60 ms; 36,752 KB
testcase_08	AC	80 ms; 40,860 KB
testcase_09	AC	156 ms; 50,712 KB
testcase_10	AC	308 ms; 60,128 KB
testcase_11	AC	196 ms; 52,788 KB
testcase_12	AC	70 ms; 36,280 KB
testcase_13	AC	83 ms; 38,688 KB
testcase_14	AC	70 ms; 39,252 KB
testcase_15	AC	42 ms; 28,628 KB
testcase_16	AC	75 ms; 38,048 KB
testcase_17	AC	430 ms; 62,884 KB
testcase_18	AC	412 ms; 66,516 KB
testcase_19	AC	412 ms; 66,640 KB
testcase_20	AC	402 ms; 67,192 KB
testcase_21	AC	414 ms; 65,976 KB
testcase_22	AC	414 ms; 65,856 KB
testcase_23	AC	403 ms; 66,960 KB
testcase_24	AC	419 ms; 66,092 KB
testcase_25	AC	417 ms; 68,624 KB
testcase_26	AC	408 ms; 64,476 KB
testcase_27	AC	271 ms; 54,140 KB
testcase_28	AC	264 ms; 54,668 KB
testcase_29	AC	270 ms; 53,068 KB
testcase_30	AC	271 ms; 53,300 KB
testcase_31	AC	280 ms; 52,956 KB
testcase_32	AC	131 ms; 62,920 KB
testcase_33	AC	132 ms; 61,296 KB
testcase_34	AC	135 ms; 65,024 KB
testcase_35	AC	137 ms; 61,020 KB
testcase_36	AC	139 ms; 63,160 KB
testcase_37	AC	46 ms; 31,184 KB
testcase_38	AC	466 ms; 53,696 KB
testcase_39	AC	303 ms; 73,280 KB
testcase_40	AC	29 ms; 27,988 KB

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

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
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 (h, w) = cin.Int2();

			var map = new HashMap<int, List<(int i, int j)>>(x => new List<(int i, int h)>()); 
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					int a = cin.Int();
					map[a].Add((i, j));
				}
			}

			var keys = map.Keys.ToArray();
			Array.Sort(keys);
			Array.Reverse(keys);

			
			var ss = new HashSet<int>();
			var tt = new HashSet<int>();
			long ans = 0;
			foreach (var k in keys) {
				if (k == 0) {
					continue;
				}

				if (map[k].Count == 1) {
					ans++;
					continue;
				}

				ss.Clear();
				tt.Clear();

				foreach (var p in map[k]) {
					ss.Add(p.i);
					tt.Add(p.j);
				}

				var compH = new Compression<int>(ss.ToArray());
				var compW = new Compression<int>(tt.ToArray());
				compH.Compress();
				compW.Compress();

				int hh = compH.Count;
				int m = compH.Count + compW.Count;
				int s = m;
				int t = m + 1;

				var flow = new MaxFlow(m + 2);
				
				foreach (var p in map[k]) {
					flow.AddEdge(compH.Zip(p.i), compW.Zip(p.j) + hh, 1);
				}

				foreach (var sss in ss) {
					flow.AddEdge(s, compH.Zip(sss), 1);
				}

				foreach (var ttt in tt) {
					flow.AddEdge(compW.Zip(ttt) + hh, t, 1);
				}

				flow.Build();

				var ret = flow.Dinic(s, t);
				ans += ret;
			}

			Console.WriteLine(ans);
		}
	}

	public class Compression<T>
		where T : IComparable<T>
	{
		public static int Compress(
			Span<T> raws,
			Func<int, T> cast)
		{
			int n = raws.Length;
			var comp = new Compression<T>(raws);
			comp.Compress();
			for (int i = 0; i < n; i++) {
				raws[i] = cast.Invoke(comp.Zip(raws[i]));
			}

			return comp.Count;
		}

		private readonly HashSet<T> raws_ = new HashSet<T>();
		private T[] values_;
		private Dictionary<T, int> map_;
		public int Count => values_.Length;

		public Compression() { }
		public Compression(ReadOnlySpan<T> values)
		{
			Add(values);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Add(T value) => raws_.Add(value);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Add(ReadOnlySpan<T> values)
		{
			foreach (var value in values) {
				raws_.Add(value);
			}
		}
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Compress(int offset = 0)
		{
			values_ = raws_.ToArray();
			Array.Sort(values_);
			map_ = new Dictionary<T, int>(values_.Length);
			int number = offset;
			for (int i = 0; i < values_.Length; ++i, ++number) {
				map_[values_[i]] = number;
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public int Zip(T value) => map_[value];
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public T UnZip(int index) => values_[index];

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public int LowerBound(T value)
		{
			int ng = -1;
			int ok = values_.Length - 1;
			while (ok - ng > 1) {
				int mid = (ok + ng) / 2;
				if (values_[mid].CompareTo(value) >= 0) {
					ok = mid;
				} else {
					ng = mid;
				}
			}

			return ok;
		}
	}

	public class MaxFlow
	{
		private const long INF = long.MaxValue;
		private readonly int n_;
		private readonly List<(int v, int index)> edgeInfos_;
		private readonly JagList2<EdgeInternal> edges_;
		private JagList2<EdgeInternal> flowedEdges_;

		public MaxFlow(int n)
		{
			n_ = n;
			edgeInfos_ = new List<(int v, int index)>();
			edges_ = new JagList2<EdgeInternal>(n);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void AddEdge(int from, int to, long capacity)
		{
			edgeInfos_.Add((from, edges_.Raw[from].Count));
			edges_.Add(from, new EdgeInternal(to, capacity, edges_.Raw[to].Count));
			edges_.Add(to, new EdgeInternal(from, 0, edges_.Raw[from].Count - 1));
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Build()
		{
			edges_.Build();
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private Edge GetFlowedEdge(int i)
		{
			var to = flowedEdges_[edgeInfos_[i].v][edgeInfos_[i].index];
			var from = flowedEdges_[to.To][to.ReverseEdgeIndex];
			return new Edge(
				edgeInfos_[i].v, to.To, (to.Capacity + from.Capacity), from.Capacity);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public ReadOnlySpan<Edge> GetFlowedEdges()
		{
			if (flowedEdges_ is null) {
				flowedEdges_ = edges_;
			}

			var result = new Edge[edgeInfos_.Count];
			for (int i = 0; i < result.Length; ++i) {
				result[i] = GetFlowedEdge(i);
			}

			return result;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long Fulkerson(int s, int t, bool keepsEdges = false)
		{
			if (keepsEdges) {
				CopyEdges();
			} else {
				flowedEdges_ = edges_;
			}

			long Dfs(int s, int t, long f, bool[] done)
			{
				if (s == t) {
					return f;
				}

				done[s] = true;
				var edges = flowedEdges_[s];
				for (int i = 0; i < edges.Length; ++i) {
					ref var edge = ref edges[i];
					if (done[edge.To] == false && edge.Capacity > 0) {
						long d = Dfs(edge.To, t, Math.Min(f, edge.Capacity), done);
						if (d > 0) {
							edge.Capacity -= d;
							flowedEdges_[edge.To][edge.ReverseEdgeIndex].Capacity += d;
							return d;
						}
					}
				}

				return 0;
			}

			long flow = 0;
			while (true) {
				var done = new bool[n_];
				long f = Dfs(s, t, INF, done);
				if (f == 0 || f == INF) {
					break;
				}

				flow += f;
			}

			return flow;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long Dinic(int s, int t, bool keepsEdges = false)
		{
			if (keepsEdges) {
				CopyEdges();
			} else {
				flowedEdges_ = edges_;
			}

			long[] Bfs(int s)
			{
				var d = new long[n_];
				d.AsSpan().Fill(-1);
				d[s] = 0;
				var q = new Queue<int>();
				q.Enqueue(s);
				while (q.Count > 0) {
					int v = q.Dequeue();
					var edges = flowedEdges_[v];
					foreach (var edge in edges) {
						if (edge.Capacity > 0 && d[edge.To] < 0) {
							d[edge.To] = d[v] + 1;
							q.Enqueue(edge.To);
						}
					}
				}

				return d;
			}

			long Dfs(int s, int t, long f, int[] done, long[] distance)
			{
				if (s == t) {
					return f;
				}

				var edges = flowedEdges_[s];
				for (; done[s] < edges.Length; done[s]++) {
					ref var edge = ref edges[done[s]];
					if (edge.Capacity > 0 && distance[s] < distance[edge.To]) {
						long d = Dfs(edge.To, t, Math.Min(f, edge.Capacity), done, distance);
						if (d > 0) {
							edge.Capacity -= d;
							flowedEdges_[edge.To][edge.ReverseEdgeIndex].Capacity += d;
							return d;
						}
					}
				}

				return 0;
			}

			long flow = 0;
			while (true) {
				var distance = Bfs(s);
				if (distance[t] < 0) {
					break;
				}

				var done = new int[n_];
				while (true) {
					long f = Dfs(s, t, INF, done, distance);
					if (f == 0 || f == INF) {
						break;
					}

					flow += f;
				}
			}

			return flow;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		private void CopyEdges()
		{
			flowedEdges_ = new JagList2<EdgeInternal>(n_);
			for (int i = 0; i < n_; ++i) {
				var edges = edges_[i];
				foreach (var edge in edges) {
					flowedEdges_.Add(i, edge);
				}
			}

			flowedEdges_.Build();
		}

		private struct EdgeInternal
		{
			public int To { get; set; }
			public int ReverseEdgeIndex { get; set; }
			public long Capacity { get; set; }
			public EdgeInternal(int to, long capacity, int reverse)
			{
				To = to;
				Capacity = capacity;
				ReverseEdgeIndex = reverse;
			}
		}

		public struct Edge
		{
			public int From { get; set; }
			public int To { get; set; }
			public long Capacity { get; set; }
			public long Flow { get; set; }
			public Edge(int from, int to, long capacity, long flow)
			{
				From = from;
				To = to;
				Capacity = capacity;
				Flow = flow;
			}
		};
	}

	public class JagList2<T> where T : struct
	{
		private readonly int n_;
		private readonly List<T>[] tempValues_;
		private T[][] values_;

		public int Count => n_;
		public List<T>[] Raw => tempValues_;
		public T[][] Values => values_;
		public T[] this[int index] => values_[index];

		public JagList2(int n)
		{
			n_ = n;
			tempValues_ = new List<T>[n];
			for (int i = 0; i < n; ++i) {
				tempValues_[i] = new List<T>();
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Add(int i, T value) => tempValues_[i].Add(value);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Build()
		{
			values_ = new T[n_][];
			for (int i = 0; i < values_.Length; ++i) {
				values_[i] = tempValues_[i].ToArray();
			}
		}
	}

	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 BitFlag ComplementOf(BitFlag sub) => flags_ & (~sub.flags_);

		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_ - 1) & flags_; sub > 0; sub = --sub & flags_) {
				action(sub);
			}
		}

		public SubBitsEnumerator SubBits => new SubBitsEnumerator(flags_);
		public struct SubBitsEnumerator : IEnumerable<BitFlag>
		{
			private readonly int flags_;
			public SubBitsEnumerator(int flags)
			{
				flags_ = flags;
			}

			IEnumerator<BitFlag> IEnumerable<BitFlag>.GetEnumerator() => new Enumerator(flags_);
			IEnumerator IEnumerable.GetEnumerator() => new Enumerator(flags_);
			public Enumerator GetEnumerator() => new Enumerator(flags_);
			public struct Enumerator : IEnumerator<BitFlag>
			{
				private readonly int src_;
				public BitFlag Current { get; private set; }
				object IEnumerator.Current => Current;

				public Enumerator(int flags)
				{
					src_ = flags;
					Current = flags;
				}

				public void Dispose() { }
				[MethodImpl(MethodImplOptions.AggressiveInlining)]
				public bool MoveNext() => (Current = --Current & src_) > 0;
				[MethodImpl(MethodImplOptions.AggressiveInlining)]
				public void Reset() => Current = src_;
			}
		}
	}

	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 static ModInt New(long value, bool mods) => new ModInt(value, mods);
		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;
			while (k > 0) {
				if ((k & 1) != 0) {
					ret = ret * value % P;
				}

				value = value * value % P;
				k >>= 1;
			}

			return new ModInt(ret);
		}

		public static Span<ModInt> NTT(Span<int> values, bool inverses = false)
			=> NumberTheoreticTransform(values, inverses);
		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> NTT(Span<long> values, bool inverses = false)
			=> NumberTheoreticTransform(values, 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> NTT(Span<ModInt> values, bool inverses = false)
			=> NumberTheoreticTransform(values, 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[,] Ntt2D(ModInt[,] a, bool inverses = false)
			=> NumberTheoreticTransform2D(a, inverses);
		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 int Pow(int n, int k)
			=> (int)Pow((long)n, (long)k);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static long Pow(long n, long k)
		{
			long ret = 1;
			long mul = n;
			while (k > 0) {
				if ((k & 1) != 0) {
					ret *= mul;
				}

				k >>= 1;
				mul *= mul;
			}

			return ret;
		}

		[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);
		}

		public static int PopCount(ulong bits)
		{
			bits = ((bits & 0xaaaaaaaaaaaaaaaa) >> 1) + (bits & 0x5555555555555555);
			bits = ((bits & 0xcccccccccccccccc) >> 2) + (bits & 0x3333333333333333);
			bits = ((bits & 0xf0f0f0f0f0f0f0f0) >> 4) + (bits & 0x0f0f0f0f0f0f0f0f);
			bits = ((bits & 0xff00ff00ff00ff00) >> 8) + (bits & 0x00ff00ff00ff00ff);
			bits = ((bits & 0xffff0000ffff0000) >> 16) + (bits & 0x0000ffff0000ffff);
			bits = ((bits & 0xffffffff00000000) >> 32) + (bits & 0x00000000ffffffff);
			return (int)bits;
		}

		[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);
		}
	}
}