結果

問題 No.5006 Hidden Maze
ユーザー takytanktakytank
提出日時 2022-06-12 15:38:35
言語 C#
(.NET 8.0.203)
結果
AC  
実行時間 138 ms / 2,000 ms
コード長 32,055 bytes
コンパイル時間 7,249 ms
実行使用メモリ 57,320 KB
スコア 66,184
平均クエリ数 338.98
最終ジャッジ日時 2022-06-12 15:38:57
合計ジャッジ時間 21,261 ms
ジャッジサーバーID
(参考情報)
judge13 / judge14
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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 72 ms
41,884 KB
testcase_01 AC 71 ms
41,692 KB
testcase_02 AC 70 ms
41,852 KB
testcase_03 AC 77 ms
43,460 KB
testcase_04 AC 78 ms
43,204 KB
testcase_05 AC 103 ms
48,560 KB
testcase_06 AC 102 ms
48,520 KB
testcase_07 AC 138 ms
53,788 KB
testcase_08 AC 94 ms
46,772 KB
testcase_09 AC 130 ms
53,988 KB
testcase_10 AC 71 ms
41,648 KB
testcase_11 AC 70 ms
41,240 KB
testcase_12 AC 79 ms
42,564 KB
testcase_13 AC 74 ms
42,432 KB
testcase_14 AC 80 ms
43,684 KB
testcase_15 AC 75 ms
43,220 KB
testcase_16 AC 87 ms
44,524 KB
testcase_17 AC 69 ms
41,080 KB
testcase_18 AC 92 ms
46,264 KB
testcase_19 AC 99 ms
46,544 KB
testcase_20 AC 74 ms
41,848 KB
testcase_21 AC 75 ms
41,888 KB
testcase_22 AC 67 ms
41,116 KB
testcase_23 AC 72 ms
41,256 KB
testcase_24 AC 76 ms
42,780 KB
testcase_25 AC 104 ms
48,628 KB
testcase_26 AC 130 ms
57,284 KB
testcase_27 AC 80 ms
43,308 KB
testcase_28 AC 132 ms
53,724 KB
testcase_29 AC 73 ms
41,264 KB
testcase_30 AC 72 ms
41,876 KB
testcase_31 AC 76 ms
42,864 KB
testcase_32 AC 93 ms
45,292 KB
testcase_33 AC 84 ms
43,796 KB
testcase_34 AC 68 ms
40,928 KB
testcase_35 AC 79 ms
43,288 KB
testcase_36 AC 76 ms
42,496 KB
testcase_37 AC 81 ms
43,676 KB
testcase_38 AC 92 ms
46,648 KB
testcase_39 AC 73 ms
41,620 KB
testcase_40 AC 69 ms
40,936 KB
testcase_41 AC 70 ms
41,188 KB
testcase_42 AC 76 ms
41,676 KB
testcase_43 AC 89 ms
44,148 KB
testcase_44 AC 71 ms
41,424 KB
testcase_45 AC 79 ms
42,192 KB
testcase_46 AC 80 ms
42,884 KB
testcase_47 AC 72 ms
41,312 KB
testcase_48 AC 127 ms
54,220 KB
testcase_49 AC 130 ms
57,320 KB
testcase_50 AC 75 ms
41,696 KB
testcase_51 AC 75 ms
41,404 KB
testcase_52 AC 69 ms
41,424 KB
testcase_53 AC 91 ms
46,108 KB
testcase_54 AC 86 ms
45,148 KB
testcase_55 AC 77 ms
41,128 KB
testcase_56 AC 79 ms
42,020 KB
testcase_57 AC 114 ms
50,024 KB
testcase_58 AC 132 ms
54,024 KB
testcase_59 AC 79 ms
42,900 KB
testcase_60 AC 70 ms
41,492 KB
testcase_61 AC 75 ms
42,120 KB
testcase_62 AC 77 ms
42,676 KB
testcase_63 AC 74 ms
41,968 KB
testcase_64 AC 81 ms
44,300 KB
testcase_65 AC 77 ms
42,900 KB
testcase_66 AC 76 ms
42,392 KB
testcase_67 AC 78 ms
42,652 KB
testcase_68 AC 84 ms
43,976 KB
testcase_69 AC 114 ms
50,576 KB
testcase_70 AC 72 ms
41,696 KB
testcase_71 AC 76 ms
42,328 KB
testcase_72 AC 93 ms
44,248 KB
testcase_73 AC 136 ms
57,072 KB
testcase_74 AC 92 ms
45,300 KB
testcase_75 AC 131 ms
54,020 KB
testcase_76 AC 113 ms
50,220 KB
testcase_77 AC 131 ms
56,824 KB
testcase_78 AC 98 ms
47,440 KB
testcase_79 AC 134 ms
53,612 KB
testcase_80 AC 74 ms
41,308 KB
testcase_81 AC 133 ms
56,856 KB
testcase_82 AC 71 ms
41,600 KB
testcase_83 AC 67 ms
41,540 KB
testcase_84 AC 69 ms
41,608 KB
testcase_85 AC 79 ms
43,252 KB
testcase_86 AC 77 ms
42,788 KB
testcase_87 AC 129 ms
57,060 KB
testcase_88 AC 86 ms
44,528 KB
testcase_89 AC 130 ms
53,924 KB
testcase_90 AC 73 ms
41,728 KB
testcase_91 AC 69 ms
41,332 KB
testcase_92 AC 82 ms
43,468 KB
testcase_93 AC 78 ms
42,208 KB
testcase_94 AC 112 ms
48,636 KB
testcase_95 AC 134 ms
55,936 KB
testcase_96 AC 68 ms
41,468 KB
testcase_97 AC 132 ms
53,844 KB
testcase_98 AC 130 ms
53,712 KB
testcase_99 AC 129 ms
53,528 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
  Determining projects to restore...
  Restored /home/judge/data/code/main.csproj (in 104 ms).
.NET 向け Microsoft (R) Build Engine バージョン 17.0.0-preview-21470-01+cb055d28f
Copyright (C) Microsoft Corporation.All rights reserved.

  プレビュー版の .NET を使用しています。https://aka.ms/dotnet-core-preview をご覧ください
  main -> /home/judge/data/code/bin/Release/net6.0/main.dll
  main -> /home/judge/data/code/bin/Release/net6.0/publish/

ソースコード

diff #

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, p) = cin.Int3();

			var blocked = new (double l, double r, double u, double d)[h, w]
				.Fill((-1, -1, -1, -1));

			double pp = (100 - p) / 100.0;
			int n = 1000;
			for (int time = 0; time < n; time++) {				
				var root = new List<Dir>();
				for (int k = -2; k <= 100; k++) {
					var prevs = new Dir[h, w].Fill(Dir.N);
					var que = new Queue<(int i, int j)>();
					que.Enqueue((0, 0));
					var dists = new int[h, w].Fill(int.MaxValue);
					dists[0, 0] = 0;
					while (que.Count > 0) {
						var (ci, cj) = que.Dequeue();
						int nd = dists[ci, cj] + 1;

						if (ci < h - 1 && blocked[ci, cj].d <= k) {
							int ni = ci + 1;
							int nj = cj;
							if (dists[ni, nj] > nd) {
								dists[ni, nj] = nd;
								que.Enqueue((ni, nj));
								prevs[ni, nj] = Dir.D;
							}
						}

						if (cj < w - 1 && blocked[ci, cj].r <= k) {
							int ni = ci;
							int nj = cj + 1;
							if (dists[ni, nj] > nd) {
								dists[ni, nj] = nd;
								que.Enqueue((ni, nj));
								prevs[ni, nj] = Dir.R;
							}
						}

						if (cj > 0 && blocked[ci, cj].l <= k) {
							int ni = ci;
							int nj = cj - 1;
							if (dists[ni, nj] > nd) {
								dists[ni, nj] = nd;
								que.Enqueue((ni, nj));
								prevs[ni, nj] = Dir.L;
							}
						}

						if (ci > 0 && blocked[ci, cj].u < k) {
							int ni = ci - 1;
							int nj = cj;
							if (dists[ni, nj] > nd) {
								dists[ni, nj] = nd;
								que.Enqueue((ni, nj));
								prevs[ni, nj] = Dir.U;
							}
						}
					}

					if (dists[h - 1, w - 1] == int.MaxValue) {
						continue;
					}

					var temp = new Stack<Dir>();
					int pi = h - 1;
					int pj = w - 1;
					while (pi != 0 || pj != 0) {
						var pre = prevs[pi, pj];
						temp.Push(pre);
						(pi, pj) = ReverseApply(pi, pj, pre);
					}

					while (temp.Count > 0) {
						root.Add(temp.Pop());
					}

					break;
				}

				var sb = new StringBuilder();
				foreach (var c in root) {
					sb.Append(c.ToString());
				}

				Console.WriteLine(sb.ToString());
				Console.Out.Flush();

				int ret = cin.Int();
				if (ret == -1) {
					return;
				}

				int ii = 0;
				int jj = 0;
				for (int k = 0; k < ret; k++) {
					var (l, r, u, d) = blocked[ii, jj];
					switch (root[k]) {
						case Dir.L:
							blocked[ii, jj] = (0, r, u, d);
							break;
						case Dir.R:
							blocked[ii, jj] = (l, 0, u, d);
							break;
						case Dir.U:
							blocked[ii, jj] = (l, r, 0, d);
							break;
						case Dir.D:
							blocked[ii, jj] = (l, r, u, 0);
							break;
						default:
							break;
					}
					(ii, jj) = Apply(ii, jj, root[k]);
				}

				{
					var (l, r, u, d) = blocked[ii, jj];
					switch (root[ret]) {
						case Dir.L:
							if (blocked[ii, jj].l < 0) {
								blocked[ii, jj] = (pp, r, u, d);
							} else {
								blocked[ii, jj] = (l * pp, r, u, d);
							}
							break;
						case Dir.R:
							if (blocked[ii, jj].r < 0) {
								blocked[ii, jj] = (l, pp, u, d);
							} else {
								blocked[ii, jj] = (l, r * pp, u, d);
							}
							break;
						case Dir.U:
							if (blocked[ii, jj].u < 0) {
								blocked[ii, jj] = (l, r, pp, d);
							} else {
								blocked[ii, jj] = (l, r, u * pp, d);
							}
							break;
						case Dir.D:
							if (blocked[ii, jj].d < 0) {
								blocked[ii, jj] = (l, r, u, pp);
							} else {
								blocked[ii, jj] = (l, r, u, d * pp);
							}
							break;
						default:
							break;
					}
				}
			}
		}

		static (int i, int j) Apply(int i, int j, Dir dir)
		{
			return dir switch {
				Dir.L => (i, j - 1),
				Dir.R => (i, j + 1),
				Dir.U => (i - 1, j),
				Dir.D => (i + 1, j),
				_ => (i, j),
			};
		}

		static (int i, int j) ReverseApply(int i, int j, Dir dir)
		{
			return dir switch {
				Dir.L => (i, j + 1),
				Dir.R => (i, j - 1),
				Dir.U => (i + 1, j),
				Dir.D => (i - 1, j),
				_ => (i, j),
			};
		}

		enum Dir
		{
			N,
			L,
			R,
			U,
			D,
		}
	}

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

		public static IEnumerable<BitFlag> All(int n)
		{
			for (var f = Begin(); f < End(n); ++f) {
				yield return f;
			}
		}

		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 int PopCount() => BitOperations.PopCount((uint)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 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 bit, int shift) => bit.flags_ << shift;
		public static BitFlag operator >>(BitFlag bit, int shift) => bit.flags_ >> shift;

		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_})";

		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 + 1;
				}

				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>
	{
		public static HashMap<TKey, TValue> Merge(
			HashMap<TKey, TValue> src1,
			HashMap<TKey, TValue> src2,
			Func<TValue, TValue, TValue> mergeValues)
		{
			if (src1.Count < src2.Count) {
				(src1, src2) = (src2, src1);
			}

			foreach (var key in src2.Keys) {
				src1[key] = mergeValues(src1[key], src2[key]);
			}

			return src1;
		}

		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 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 class DijkstraQ
	{
		private int count_ = 0;
		private long[] distanceHeap_;
		private int[] vertexHeap_;

		public int Count => count_;
		public DijkstraQ()
		{
			distanceHeap_ = new long[8];
			vertexHeap_ = new int[8];
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public void Enqueue(long distance, int v)
		{
			if (distanceHeap_.Length == count_) {
				var newDistanceHeap = new long[distanceHeap_.Length << 1];
				var newVertexHeap = new int[vertexHeap_.Length << 1];
				Unsafe.CopyBlock(
					ref Unsafe.As<long, byte>(ref newDistanceHeap[0]),
					ref Unsafe.As<long, byte>(ref distanceHeap_[0]),
					(uint)(8 * count_));
				Unsafe.CopyBlock(
					ref Unsafe.As<int, byte>(ref newVertexHeap[0]),
					ref Unsafe.As<int, byte>(ref vertexHeap_[0]),
					(uint)(4 * count_));
				distanceHeap_ = newDistanceHeap;
				vertexHeap_ = newVertexHeap;
			}

			ref var dRef = ref distanceHeap_[0];
			ref var vRef = ref vertexHeap_[0];
			Unsafe.Add(ref dRef, count_) = distance;
			Unsafe.Add(ref vRef, count_) = v;
			++count_;

			int c = count_ - 1;
			while (c > 0) {
				int p = (c - 1) >> 1;
				var tempD = Unsafe.Add(ref dRef, p);
				if (tempD <= distance) {
					break;
				} else {
					Unsafe.Add(ref dRef, c) = tempD;
					Unsafe.Add(ref vRef, c) = Unsafe.Add(ref vRef, p);
					c = p;
				}
			}

			Unsafe.Add(ref dRef, c) = distance;
			Unsafe.Add(ref vRef, c) = v;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (long distance, int v) Dequeue()
		{
			ref var dRef = ref distanceHeap_[0];
			ref var vRef = ref vertexHeap_[0];
			(long distance, int v) ret = (dRef, vRef);
			int n = count_ - 1;

			var distance = Unsafe.Add(ref dRef, n);
			var vertex = Unsafe.Add(ref vRef, n);
			int p = 0;
			int c = (p << 1) + 1;
			while (c < n) {
				if (c != n - 1 && Unsafe.Add(ref dRef, c + 1) < Unsafe.Add(ref dRef, c)) {
					++c;
				}

				var tempD = Unsafe.Add(ref dRef, c);
				if (distance > tempD) {
					Unsafe.Add(ref dRef, p) = tempD;
					Unsafe.Add(ref vRef, p) = Unsafe.Add(ref vRef, c);
					p = c;
					c = (p << 1) + 1;
				} else {
					break;
				}
			}

			Unsafe.Add(ref dRef, p) = distance;
			Unsafe.Add(ref vRef, p) = vertex;
			--count_;

			return ret;
		}
	}

	public struct ModInt
	{
		public const long P = 1000000007;
		//public const long P = 998244353;
		//public const long P = 2;
		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)
			=> lhs * Inverse(rhs);

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

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static ModInt Inverse(ModInt value) => Pow(value, P - 2);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static ModInt Pow(ModInt value, long k) => Pow(value.value_, k);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		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);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public long ToLong() => value_;
		public override string ToString() => value_.ToString();
	}

	public static class Helper
	{
		public static long INF => 1L << 50;

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T Clamp<T>(this T value, T min, T max) where T : struct, IComparable<T>
		{
			if (value.CompareTo(min) <= 0) {
				return min;
			}

			if (value.CompareTo(max) >= 0) {
				return max;
			}

			return value;
		}

		[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 long BinarySearchOKNG(long ok, long ng, Func<long, bool> satisfies)
		{
			while (ng - ok > 1) {
				long mid = (ok + ng) / 2;
				if (satisfies(mid)) {
					ok = mid;
				} else {
					ng = mid;
				}
			}

			return ok;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static long BinarySearchNGOK(long ng, long ok, Func<long, bool> satisfies)
		{
			while (ok - ng > 1) {
				long mid = (ok + ng) / 2;
				if (satisfies(mid)) {
					ok = mid;
				} else {
					ng = mid;
				}
			}

			return ok;
		}

		[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));

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static T[] Merge<T>(ReadOnlySpan<T> first, ReadOnlySpan<T> second) where T : IComparable<T>
		{
			var ret = new T[first.Length + second.Length];
			int p = 0;
			int q = 0;
			while (p < first.Length || q < second.Length) {
				if (p == first.Length) {
					ret[p + q] = second[q];
					q++;
					continue;
				}

				if (q == second.Length) {
					ret[p + q] = first[p];
					p++;
					continue;
				}

				if (first[p].CompareTo(second[q]) < 0) {
					ret[p + q] = first[p];
					p++;
				} else {
					ret[p + q] = second[q];
					q++;
				}
			}

			return ret;
		}

		private static readonly int[] delta4_ = { 1, 0, -1, 0, 1 };
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static IEnumerable<(int i, int j)> Adjacence4(int i, int j, int imax, int jmax)
		{
			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) {
					yield return (d4i, d4j);
				}
			}
		}

		private static readonly int[] delta8_ = { 1, 0, -1, 0, 1, 1, -1, -1, 1 };
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static IEnumerable<(int i, int j)> Adjacence8(int i, int j, int imax, int jmax)
		{
			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) {
					yield return (d8i, d8j);
				}
			}
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static IEnumerable<int> SubBitsOf(int bit)
		{
			for (int sub = bit; sub > 0; sub = --sub & bit) {
				yield return 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 Exchange(string src, char a, char b)
		{
			var chars = src.ToCharArray();
			for (int i = 0; i < chars.Length; i++) {
				if (chars[i] == a) {
					chars[i] = b;
				} else if (chars[i] == b) {
					chars[i] = a;
				}
			}

			return new string(chars);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static void Swap(this string str, int i, int j)
		{
			var span = str.AsWriteableSpan();
			(span[i], span[j]) = (span[j], span[i]);
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static char Replace(this string str, int index, char c)
		{
			var span = str.AsWriteableSpan();
			char old = span[index];
			span[index] = c;
			return old;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<char> AsWriteableSpan(this string str)
		{
			var span = str.AsSpan();
			return MemoryMarshal.CreateSpan(ref MemoryMarshal.GetReference(span), span.Length);
		}

		[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
	{
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public static Span<T> AsSpan<T>(this List<T> list)
		{
			return Unsafe.As<FakeList<T>>(list).Array.AsSpan(0, list.Count);
		}

		private class FakeList<T>
		{
			public T[] Array = null;
		}
	}

	public class Scanner : IDisposable
	{
		private const int BUFFER_SIZE = 1024;
		private const int ASCII_SPACE = 32;
		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 string NextLine()
		{
			var sb = new StringBuilder();
			for (var b = Char(); b >= ASCII_SPACE && b <= ASCII_CHAR_END; b = (char)Read()) {
				sb.Append(b);
			}

			return sb.ToString();
		}


		[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 String()
		{
			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] = String();
			}

			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, int, int, int, int) Int5(int offset = 0)
			=> (Int(offset), 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, long, long, long, long) Long5(long offset = 0)
			=> (Long(offset), 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, BigInteger, BigInteger, BigInteger, BigInteger) Big5(long offset = 0)
			=> (Big(offset), 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(String(), 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, double, double, double, double) Double5(double offset = 0)
			=> (Double(offset), 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;
		}

		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public decimal Decimal() => decimal.Parse(String(), CultureInfo.InvariantCulture);
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public decimal Decimal(decimal offset) => Decimal() + offset;
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (decimal, decimal) Decimal2(decimal offset = 0)
			=> (Decimal(offset), Decimal(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (decimal, decimal, decimal) Decimal3(decimal offset = 0)
			=> (Decimal(offset), Decimal(offset), Decimal(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (decimal, decimal, decimal, decimal) Decimal4(decimal offset = 0)
			=> (Decimal(offset), Decimal(offset), Decimal(offset), Decimal(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public (decimal, decimal, decimal, decimal, decimal) Decimal5(decimal offset = 0)
			=> (Decimal(offset), Decimal(offset), Decimal(offset), Decimal(offset), Decimal(offset));
		[MethodImpl(MethodImplOptions.AggressiveInlining)]
		public decimal[] ArrayDecimal(int length, decimal offset = 0)
		{
			var array = new decimal[length];
			for (int i = 0; i < length; ++i) {
				array[i] = Decimal(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);
		}
	}
}
0