結果
| 問題 |
No.1307 Rotate and Accumulate
|
| ユーザー |
 takytank
|
| 提出日時 | 2020-12-04 01:19:55 |
| 言語 | C#(csc) (csc 3.9.0) |
| 結果 |
AC
|
| 実行時間 | 1,132 ms / 5,000 ms |
| コード長 | 58,829 bytes |
| コンパイル時間 | 3,451 ms |
| コンパイル使用メモリ | 124,160 KB |
| 実行使用メモリ | 36,864 KB |
| 最終ジャッジ日時 | 2024-09-14 11:24:37 |
| 合計ジャッジ時間 | 16,018 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge6 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 19 |
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.Diagnostics.CodeAnalysis;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Reflection.Metadata;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Text;
using System.Threading;
namespace YukiCoder
{
public 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 = Math.ConvolutionLong(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 partial class Math
{
/// <summary>
/// 畳み込みを mod <paramref name="m"/> = 998244353 で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<paramref name="m"/>≤2×10^9</para>
/// <para>- <paramref name="m"/> は素数</para>
/// <para>- 2^c | (<paramref name="m"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<paramref name="m"/>)</para>
/// </remarks>
public static int[] Convolution(int[] a, int[] b) => Convolution<Mod998244353>(a, b);
/// <summary>
/// 畳み込みを mod <paramref name="m"/> = 998244353 で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<paramref name="m"/>≤2×10^9</para>
/// <para>- <paramref name="m"/> は素数</para>
/// <para>- 2^c | (<paramref name="m"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<paramref name="m"/>)</para>
/// </remarks>
public static uint[] Convolution(uint[] a, uint[] b) => Convolution<Mod998244353>(a, b);
/// <summary>
/// 畳み込みを mod <paramref name="m"/> = 998244353 で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<paramref name="m"/>≤2×10^9</para>
/// <para>- <paramref name="m"/> は素数</para>
/// <para>- 2^c | (<paramref name="m"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<paramref name="m"/>)</para>
/// </remarks>
public static long[] Convolution(long[] a, long[] b) => Convolution<Mod998244353>(a, b);
/// <summary>
/// 畳み込みを mod <paramref name="m"/> = 998244353 で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<paramref name="m"/>≤2×10^9</para>
/// <para>- <paramref name="m"/> は素数</para>
/// <para>- 2^c | (<paramref name="m"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<paramref name="m"/>)</para>
/// </remarks>
public static ulong[] Convolution(ulong[] a, ulong[] b) => Convolution<Mod998244353>(a, b);
/// <summary>
/// 畳み込みを mod <typeparamref name="TMod"/> で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<typeparamref name="TMod"/>≤2×10^9</para>
/// <para>- <typeparamref name="TMod"/> は素数</para>
/// <para>- 2^c | (<typeparamref name="TMod"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<typeparamref name="TMod"/>)</para>
/// </remarks>
public static int[] Convolution<TMod>(int[] a, int[] b) where TMod : struct, IStaticMod
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 0) {
return Array.Empty<int>();
}
if (System.Math.Min(n, m) <= 60) {
var c = ConvolutionNaive<TMod>(a.Select(ai => new StaticModInt<TMod>(ai)).ToArray(),
b.Select(bi => new StaticModInt<TMod>(bi)).ToArray());
return c.Select(ci => ci.Value).ToArray();
} else {
int z = 1 << InternalMath.CeilPow2(n + m - 1);
var aTemp = new StaticModInt<TMod>[z];
for (int i = 0; i < a.Length; i++) {
aTemp[i] = new StaticModInt<TMod>(a[i]);
}
var bTemp = new StaticModInt<TMod>[z];
for (int i = 0; i < b.Length; i++) {
bTemp[i] = new StaticModInt<TMod>(b[i]);
}
var c = Convolution<TMod>(aTemp, bTemp, n, m, z)[0..(n + m - 1)];
var result = new int[c.Length];
for (int i = 0; i < result.Length; i++) {
result[i] = c[i].Value;
}
return result;
}
}
/// <summary>
/// 畳み込みを mod <typeparamref name="TMod"/> で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<typeparamref name="TMod"/>≤2×10^9</para>
/// <para>- <typeparamref name="TMod"/> は素数</para>
/// <para>- 2^c | (<typeparamref name="TMod"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<typeparamref name="TMod"/>)</para>
/// </remarks>
public static uint[] Convolution<TMod>(uint[] a, uint[] b) where TMod : struct, IStaticMod
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 0) {
return Array.Empty<uint>();
}
if (System.Math.Min(n, m) <= 60) {
var c = ConvolutionNaive<TMod>(a.Select(ai => new StaticModInt<TMod>(ai)).ToArray(),
b.Select(bi => new StaticModInt<TMod>(bi)).ToArray());
return c.Select(ci => (uint)ci.Value).ToArray();
} else {
int z = 1 << InternalMath.CeilPow2(n + m - 1);
var aTemp = new StaticModInt<TMod>[z];
for (int i = 0; i < a.Length; i++) {
aTemp[i] = new StaticModInt<TMod>(a[i]);
}
var bTemp = new StaticModInt<TMod>[z];
for (int i = 0; i < b.Length; i++) {
bTemp[i] = new StaticModInt<TMod>(b[i]);
}
var c = Convolution<TMod>(aTemp, bTemp, n, m, z)[0..(n + m - 1)];
var result = new uint[c.Length];
for (int i = 0; i < result.Length; i++) {
result[i] = (uint)c[i].Value;
}
return result;
}
}
/// <summary>
/// 畳み込みを mod <typeparamref name="TMod"/> で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<typeparamref name="TMod"/>≤2×10^9</para>
/// <para>- <typeparamref name="TMod"/> は素数</para>
/// <para>- 2^c | (<typeparamref name="TMod"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<typeparamref name="TMod"/>)</para>
/// </remarks>
public static long[] Convolution<TMod>(long[] a, long[] b) where TMod : struct, IStaticMod
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 0) {
return Array.Empty<long>();
}
if (System.Math.Min(n, m) <= 60) {
var c = ConvolutionNaive<TMod>(a.Select(ai => new StaticModInt<TMod>(ai)).ToArray(),
b.Select(bi => new StaticModInt<TMod>(bi)).ToArray());
return c.Select(ci => (long)ci.Value).ToArray();
} else {
int z = 1 << InternalMath.CeilPow2(n + m - 1);
var aTemp = new StaticModInt<TMod>[z];
for (int i = 0; i < a.Length; i++) {
aTemp[i] = new StaticModInt<TMod>(a[i]);
}
var bTemp = new StaticModInt<TMod>[z];
for (int i = 0; i < b.Length; i++) {
bTemp[i] = new StaticModInt<TMod>(b[i]);
}
var c = Convolution<TMod>(aTemp, bTemp, n, m, z)[0..(n + m - 1)];
var result = new long[c.Length];
for (int i = 0; i < result.Length; i++) {
result[i] = c[i].Value;
}
return result;
}
}
/// <summary>
/// 畳み込みを mod <typeparamref name="TMod"/> で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<typeparamref name="TMod"/>≤2×10^9</para>
/// <para>- <typeparamref name="TMod"/> は素数</para>
/// <para>- 2^c | (<typeparamref name="TMod"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<typeparamref name="TMod"/>)</para>
/// </remarks>
public static ulong[] Convolution<TMod>(ulong[] a, ulong[] b) where TMod : struct, IStaticMod
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 0) {
return Array.Empty<ulong>();
}
if (System.Math.Min(n, m) <= 60) {
var c = ConvolutionNaive<TMod>(a.Select(TakeMod).ToArray(),
b.Select(TakeMod).ToArray());
return c.Select(ci => (ulong)ci.Value).ToArray();
} else {
int z = 1 << InternalMath.CeilPow2(n + m - 1);
var aTemp = new StaticModInt<TMod>[z];
for (int i = 0; i < a.Length; i++) {
aTemp[i] = TakeMod(a[i]);
}
var bTemp = new StaticModInt<TMod>[z];
for (int i = 0; i < b.Length; i++) {
bTemp[i] = TakeMod(b[i]);
}
var c = Convolution<TMod>(aTemp, bTemp, n, m, z)[0..(n + m - 1)];
var result = new ulong[c.Length];
for (int i = 0; i < result.Length; i++) {
result[i] = (ulong)c[i].Value;
}
return result;
}
StaticModInt<TMod> TakeMod(ulong x) => StaticModInt<TMod>.Raw((int)(x % default(TMod).Mod));
}
/// <summary>
/// 畳み込みを mod <typeparamref name="TMod"/> で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<typeparamref name="TMod"/>≤2×10^9</para>
/// <para>- <typeparamref name="TMod"/> は素数</para>
/// <para>- 2^c | (<typeparamref name="TMod"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<typeparamref name="TMod"/>)</para>
/// </remarks>
public static StaticModInt<TMod>[] Convolution<TMod>(StaticModInt<TMod>[] a, StaticModInt<TMod>[] b)
where TMod : struct, IStaticMod
{
var temp = Convolution((ReadOnlySpan<StaticModInt<TMod>>)a, b);
return temp.ToArray();
}
/// <summary>
/// 畳み込みを mod <typeparamref name="TMod"/> で計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- 2≤<typeparamref name="TMod"/>≤2×10^9</para>
/// <para>- <typeparamref name="TMod"/> は素数</para>
/// <para>- 2^c | (<typeparamref name="TMod"/> - 1) かつ |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^c なる c が存在する</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|) + log<typeparamref name="TMod"/>)</para>
/// </remarks>
public static Span<StaticModInt<TMod>> Convolution<TMod>(ReadOnlySpan<StaticModInt<TMod>> a, ReadOnlySpan<StaticModInt<TMod>> b)
where TMod : struct, IStaticMod
{
var n = a.Length;
var m = b.Length;
if (n == 0 || m == 0) {
return Array.Empty<StaticModInt<TMod>>();
}
if (System.Math.Min(n, m) <= 60) {
return ConvolutionNaive(a, b);
}
int z = 1 << InternalMath.CeilPow2(n + m - 1);
var aTemp = new StaticModInt<TMod>[z];
a.CopyTo(aTemp);
var bTemp = new StaticModInt<TMod>[z];
b.CopyTo(bTemp);
return Convolution(aTemp.AsSpan(), bTemp.AsSpan(), n, m, z);
}
private static Span<StaticModInt<TMod>> Convolution<TMod>(Span<StaticModInt<TMod>> a, Span<StaticModInt<TMod>> b, int n, int m, int z)
where TMod : struct, IStaticMod
{
Butterfly<TMod>.Calculate(a);
Butterfly<TMod>.Calculate(b);
for (int i = 0; i < a.Length; i++) {
a[i] *= b[i];
}
Butterfly<TMod>.CalculateInv(a);
var result = a[0..(n + m - 1)];
var iz = new StaticModInt<TMod>(z).Inv();
foreach (ref var r in result) {
r *= iz;
}
return result;
}
/// <summary>
/// 畳み込みを計算します。
/// </summary>
/// <remarks>
/// <para><paramref name="a"/>, <paramref name="b"/> の少なくとも一方が空の場合は空配列を返します。</para>
/// <para>制約:</para>
/// <para>- |<paramref name="a"/>| + |<paramref name="b"/>| - 1 ≤ 2^24 = 16,777,216</para>
/// <para>- 畳み込んだ後の配列の要素が全て long に収まる</para>
/// <para>計算量: O((|<paramref name="a"/>|+|<paramref name="b"/>|)log(|<paramref name="a"/>|+|<paramref name="b"/>|))</para>
/// </remarks>
public static long[] ConvolutionLong(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 = 754974721;
const ulong Mod2 = 167772161;
const ulong Mod3 = 469762049;
const ulong M2M3 = Mod2 * Mod3;
const ulong M1M3 = Mod1 * Mod3;
const ulong M1M2 = Mod1 * Mod2;
// (m1 * m2 * m3) % 2^64
const ulong M1M2M3 = Mod1 * Mod2 * Mod3;
ulong i1 = (ulong)InternalMath.InvGCD((long)M2M3, (long)Mod1).Item2;
ulong i2 = (ulong)InternalMath.InvGCD((long)M1M3, (long)Mod2).Item2;
ulong i3 = (ulong)InternalMath.InvGCD((long)M1M2, (long)Mod3).Item2;
var c1 = Convolution<FFTMod1>(a, b);
var c2 = Convolution<FFTMod2>(a, b);
var c3 = Convolution<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] - InternalMath.SafeMod((long)x, (long)Mod1);
if (diff < 0) {
diff += (long)Mod1;
}
// 真値を r, 得られた値を x, M1M2M3 % 2^64 = M', B = 2^63 として、
// r = x,
// x - M' + (0 or 2B),
// x - 2M' + (0 or 2B or 4B),
// x - 3M' + (0 or 2B or 4B or 6B)
// のいずれかが成り立つ、らしい
// -> see atcoder/convolution.hpp
x -= offset[(int)(diff % offset.Length)];
c[i] = (long)x;
}
return c;
}
ulong[] Convolution<TMod>(ReadOnlySpan<long> a, ReadOnlySpan<long> b) where TMod : struct, IStaticMod
{
int z = 1 << InternalMath.CeilPow2(a.Length + b.Length - 1);
var aTemp = new StaticModInt<TMod>[z];
for (int i = 0; i < a.Length; i++) {
aTemp[i] = new StaticModInt<TMod>(a[i]);
}
var bTemp = new StaticModInt<TMod>[z];
for (int i = 0; i < b.Length; i++) {
bTemp[i] = new StaticModInt<TMod>(b[i]);
}
var c = YukiCoder.Math.Convolution<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;
}
}
private static StaticModInt<TMod>[] ConvolutionNaive<TMod>(ReadOnlySpan<StaticModInt<TMod>> a, ReadOnlySpan<StaticModInt<TMod>> b)
where TMod : struct, IStaticMod
{
if (a.Length < b.Length) {
// ref 構造体のため型引数として使えない
var temp = a;
a = b;
b = temp;
}
var ans = new StaticModInt<TMod>[a.Length + b.Length - 1];
for (int i = 0; i < a.Length; i++) {
for (int j = 0; j < b.Length; j++) {
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
private readonly struct FFTMod1 : IStaticMod
{
public uint Mod => 754974721;
public bool IsPrime => true;
}
private readonly struct FFTMod2 : IStaticMod
{
public uint Mod => 167772161;
public bool IsPrime => true;
}
private readonly struct FFTMod3 : IStaticMod
{
public uint Mod => 469762049;
public bool IsPrime => true;
}
}
/// <summary>
/// コンパイル時に決定する mod を表します。
/// </summary>
/// <example>
/// <code>
/// public readonly struct Mod1000000009 : IStaticMod
/// {
/// public uint Mod => 1000000009;
/// public bool IsPrime => true;
/// }
/// </code>
/// </example>
public interface IStaticMod
{
/// <summary>
/// mod を取得します。
/// </summary>
uint Mod { get; }
/// <summary>
/// mod が素数であるか識別します。
/// </summary>
bool IsPrime { get; }
}
public readonly struct Mod1000000007 : IStaticMod
{
public uint Mod => 1000000007;
public bool IsPrime => true;
}
public readonly struct Mod998244353 : IStaticMod
{
public uint Mod => 998244353;
public bool IsPrime => true;
}
/// <summary>
/// 実行時に決定する mod の ID を表します。
/// </summary>
/// <example>
/// <code>
/// public readonly struct ModID123 : IDynamicModID { }
/// </code>
/// </example>
public interface IDynamicModID { }
public readonly struct ModID0 : IDynamicModID { }
public readonly struct ModID1 : IDynamicModID { }
public readonly struct ModID2 : IDynamicModID { }
/// <summary>
/// 四則演算時に自動で mod を取る整数型。mod の値はコンパイル時に決定している必要があります。
/// </summary>
/// <typeparam name="T">定数 mod を表す構造体</typeparam>
/// <example>
/// <code>
/// using ModInt = AtCoder.StaticModInt<AtCoder.Mod1000000007>;
///
/// void SomeMethod()
/// {
/// var m = new ModInt(1);
/// m -= 2;
/// Console.WriteLine(m); // 1000000006
/// }
/// </code>
/// </example>
public readonly struct StaticModInt<T> where T : struct, IStaticMod
{
private readonly uint _v;
/// <summary>
/// 格納されている値を返します。
/// </summary>
public int Value => (int)_v;
/// <summary>
/// mod を返します。
/// </summary>
public static int Mod => (int)default(T).Mod;
/// <summary>
/// <paramref name="v"/> に対して mod を取らずに StaticModInt<<typeparamref name="T"/>> 型のインスタンスを生成します。
/// </summary>
/// <remarks>
/// <para>定数倍高速化のための関数です。 <paramref name="v"/> に 0 未満または mod 以上の値を入れた場合の挙動は未定義です。</para>
/// <para>制約: 0≤|<paramref name="v"/>|<mod</para>
/// </remarks>
public static StaticModInt<T> Raw(int v)
{
var u = unchecked((uint)v);
Debug.Assert(u < Mod);
return new StaticModInt<T>(u);
}
/// <summary>
/// StaticModInt<<typeparamref name="T"/>> 型のインスタンスを生成します。
/// </summary>
/// <remarks>
/// <paramref name="v"/>が 0 未満、もしくは mod 以上の場合、自動で mod を取ります。
/// </remarks>
public StaticModInt(long v) : this(Round(v)) { }
private StaticModInt(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 StaticModInt<T> operator ++(StaticModInt<T> value)
{
var v = value._v + 1;
if (v == default(T).Mod) {
v = 0;
}
return new StaticModInt<T>(v);
}
public static StaticModInt<T> operator --(StaticModInt<T> value)
{
var v = value._v;
if (v == 0) {
v = default(T).Mod;
}
return new StaticModInt<T>(v - 1);
}
public static StaticModInt<T> operator +(StaticModInt<T> lhs, StaticModInt<T> rhs)
{
var v = lhs._v + rhs._v;
if (v >= default(T).Mod) {
v -= default(T).Mod;
}
return new StaticModInt<T>(v);
}
public static StaticModInt<T> operator -(StaticModInt<T> lhs, StaticModInt<T> rhs)
{
unchecked {
var v = lhs._v - rhs._v;
if (v >= default(T).Mod) {
v += default(T).Mod;
}
return new StaticModInt<T>(v);
}
}
public static StaticModInt<T> operator *(StaticModInt<T> lhs, StaticModInt<T> rhs)
{
return new StaticModInt<T>((uint)((ulong)lhs._v * rhs._v % default(T).Mod));
}
/// <summary>
/// 除算を行います。
/// </summary>
/// <remarks>
/// <para>- 制約: <paramref name="rhs"/> に乗法の逆元が存在する。（gcd(<paramref name="rhs"/>, mod) = 1）</para>
/// <para>- 計算量: O(log(mod))</para>
/// </remarks>
public static StaticModInt<T> operator /(StaticModInt<T> lhs, StaticModInt<T> rhs) => lhs * rhs.Inv();
public static StaticModInt<T> operator +(StaticModInt<T> value) => value;
public static StaticModInt<T> operator -(StaticModInt<T> value) => new StaticModInt<T>() - value;
public static bool operator ==(StaticModInt<T> lhs, StaticModInt<T> rhs) => lhs._v == rhs._v;
public static bool operator !=(StaticModInt<T> lhs, StaticModInt<T> rhs) => lhs._v != rhs._v;
public static implicit operator StaticModInt<T>(int value) => new StaticModInt<T>(value);
public static implicit operator StaticModInt<T>(long value) => new StaticModInt<T>(value);
/// <summary>
/// 自身を x として、x^<paramref name="n"/> を返します。
/// </summary>
/// <remarks>
/// <para>制約: 0≤|<paramref name="n"/>|</para>
/// <para>計算量: O(log(<paramref name="n"/>))</para>
/// </remarks>
public StaticModInt<T> Pow(long n)
{
Debug.Assert(0 <= n);
var x = this;
var r = new StaticModInt<T>(1u);
while (n > 0) {
if ((n & 1) > 0) {
r *= x;
}
x *= x;
n >>= 1;
}
return r;
}
/// <summary>
/// 自身を x として、 xy≡1 なる y を返します。
/// </summary>
/// <remarks>
/// <para>制約: gcd(x, mod) = 1</para>
/// </remarks>
public StaticModInt<T> Inv()
{
if (default(T).IsPrime) {
Debug.Assert(_v > 0);
return Pow(default(T).Mod - 2);
} else {
var (g, x) = InternalMath.InvGCD(_v, default(T).Mod);
Debug.Assert(g == 1);
return new StaticModInt<T>(x);
}
}
public override string ToString() => _v.ToString();
public override bool Equals(object obj) => obj is StaticModInt<T> && this == (StaticModInt<T>)obj;
public override int GetHashCode() => _v.GetHashCode();
}
/// <summary>
/// 四則演算時に自動で mod を取る整数型。実行時に mod が決まる場合でも使用可能です。
/// </summary>
/// <remarks>
/// 使用前に DynamicModInt<<typeparamref name="T"/>>.Mod に mod の値を設定する必要があります。
/// </remarks>
/// <typeparam name="T">mod の ID を表す構造体</typeparam>
/// <example>
/// <code>
/// using AtCoder.ModInt = AtCoder.DynamicModInt<AtCoder.ModID0>;
///
/// void SomeMethod()
/// {
/// ModInt.Mod = 1000000009;
/// var m = new ModInt(1);
/// m -= 2;
/// Console.WriteLine(m); // 1000000008
/// }
/// </code>
/// </example>
public readonly struct DynamicModInt<T> where T : struct, IDynamicModID
{
private readonly uint _v;
private static Barrett bt;
/// <summary>
/// 格納されている値を返します。
/// </summary>
public int Value => (int)_v;
/// <summary>
/// mod を返します。
/// </summary>
public static int Mod
{
get => (int)bt.Mod;
set
{
Debug.Assert(1 <= value);
bt = new Barrett((uint)value);
}
}
/// <summary>
/// <paramref name="v"/> に対して mod を取らずに DynamicModInt<<typeparamref name="T"/>> 型のインスタンスを生成します。
/// </summary>
/// <remarks>
/// <para>定数倍高速化のための関数です。 <paramref name="v"/> に 0 未満または mod 以上の値を入れた場合の挙動は未定義です。</para>
/// <para>制約: 0≤|<paramref name="v"/>|<mod</para>
/// </remarks>
public static DynamicModInt<T> Raw(int v)
{
var u = unchecked((uint)v);
Debug.Assert(bt != null, $"使用前に {nameof(DynamicModInt<T>)}<{nameof(T)}>.{nameof(Mod)} プロパティに mod の値を設定してください。");
Debug.Assert(u < Mod);
return new DynamicModInt<T>(u);
}
/// <summary>
/// DynamicModInt<<typeparamref name="T"/>> 型のインスタンスを生成します。
/// </summary>
/// <remarks>
/// <para>- 使用前に DynamicModInt<<typeparamref name="T"/>>.Mod に mod の値を設定する必要があります。</para>
/// <para>- <paramref name="v"/> が 0 未満、もしくは mod 以上の場合、自動で mod を取ります。</para>
/// </remarks>
public DynamicModInt(long v) : this(Round(v)) { }
private DynamicModInt(uint v) => _v = v;
private static uint Round(long v)
{
Debug.Assert(bt != null, $"使用前に {nameof(DynamicModInt<T>)}<{nameof(T)}>.{nameof(Mod)} プロパティに mod の値を設定してください。");
var x = v % bt.Mod;
if (x < 0) {
x += bt.Mod;
}
return (uint)x;
}
public static DynamicModInt<T> operator ++(DynamicModInt<T> value)
{
var v = value._v + 1;
if (v == bt.Mod) {
v = 0;
}
return new DynamicModInt<T>(v);
}
public static DynamicModInt<T> operator --(DynamicModInt<T> value)
{
var v = value._v;
if (v == 0) {
v = bt.Mod;
}
return new DynamicModInt<T>(v - 1);
}
public static DynamicModInt<T> operator +(DynamicModInt<T> lhs, DynamicModInt<T> rhs)
{
var v = lhs._v + rhs._v;
if (v >= bt.Mod) {
v -= bt.Mod;
}
return new DynamicModInt<T>(v);
}
public static DynamicModInt<T> operator -(DynamicModInt<T> lhs, DynamicModInt<T> rhs)
{
unchecked {
var v = lhs._v - rhs._v;
if (v >= bt.Mod) {
v += bt.Mod;
}
return new DynamicModInt<T>(v);
}
}
public static DynamicModInt<T> operator *(DynamicModInt<T> lhs, DynamicModInt<T> rhs)
{
uint z = bt.Mul(lhs._v, rhs._v);
return new DynamicModInt<T>(z);
}
/// <summary>
/// 除算を行います。
/// </summary>
/// <remarks>
/// <para>- 制約: <paramref name="rhs"/> に乗法の逆元が存在する。（gcd(<paramref name="rhs"/>, mod) = 1）</para>
/// <para>- 計算量: O(log(mod))</para>
/// </remarks>
public static DynamicModInt<T> operator /(DynamicModInt<T> lhs, DynamicModInt<T> rhs) => lhs * rhs.Inv();
public static DynamicModInt<T> operator +(DynamicModInt<T> value) => value;
public static DynamicModInt<T> operator -(DynamicModInt<T> value) => new DynamicModInt<T>() - value;
public static bool operator ==(DynamicModInt<T> lhs, DynamicModInt<T> rhs) => lhs._v == rhs._v;
public static bool operator !=(DynamicModInt<T> lhs, DynamicModInt<T> rhs) => lhs._v != rhs._v;
public static implicit operator DynamicModInt<T>(int value) => new DynamicModInt<T>(value);
public static implicit operator DynamicModInt<T>(long value) => new DynamicModInt<T>(value);
/// <summary>
/// 自身を x として、x^<paramref name="n"/> を返します。
/// </summary>
/// <remarks>
/// <para>制約: 0≤|<paramref name="n"/>|</para>
/// <para>計算量: O(log(<paramref name="n"/>))</para>
/// </remarks>
public DynamicModInt<T> Pow(long n)
{
Debug.Assert(0 <= n);
var x = this;
var r = new DynamicModInt<T>(1u);
while (n > 0) {
if ((n & 1) > 0) {
r *= x;
}
x *= x;
n >>= 1;
}
return r;
}
/// <summary>
/// 自身を x として、 xy≡1 なる y を返します。
/// </summary>
/// <remarks>
/// <para>制約: gcd(x, mod) = 1</para>
/// </remarks>
public DynamicModInt<T> Inv()
{
var (g, x) = InternalMath.InvGCD(_v, bt.Mod);
Debug.Assert(g == 1);
return new DynamicModInt<T>(x);
}
public override string ToString() => _v.ToString();
public override bool Equals(object obj) => obj is DynamicModInt<T> && this == (DynamicModInt<T>)obj;
public override int GetHashCode() => _v.GetHashCode();
}
public static partial class InternalMath
{
private static readonly Dictionary<int, int> primitiveRootsCache = new Dictionary<int, int>()
{
{ 2, 1 },
{ 167772161, 3 },
{ 469762049, 3 },
{ 754974721, 11 },
{ 998244353, 3 }
};
/// <summary>
/// <paramref name="m"/> の最小の原始根を求めます。
/// </summary>
/// <remarks>
/// 制約: <paramref name="m"/> は素数
/// </remarks>
public static int PrimitiveRoot(int m)
{
Debug.Assert(m >= 2);
if (primitiveRootsCache.TryGetValue(m, out var p)) {
return p;
}
return primitiveRootsCache[m] = Calculate(m);
int Calculate(int m)
{
Span<int> divs = stackalloc int[20];
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) {
x >>= 1;
}
for (int i = 3; (long)i * i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2; ; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (PowMod(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) {
return g;
}
}
}
}
/// <summary>
/// <paramref name="x"/>^<paramref name="n"/> mod <paramref name="m"/> を返します。
/// </summary>
/// <remarks>
/// <para>制約: 0≤<paramref name="n"/>, 1≤<paramref name="m"/></para>
/// <para>計算量: O(log<paramref name="n"/>)</para>
/// </remarks>
public static long PowMod(long x, long n, int m)
{
Debug.Assert(0 <= n && 1 <= m);
if (m == 1) return 0;
Barrett barrett = new Barrett((uint)m);
uint r = 1, y = (uint)InternalMath.SafeMod(x, m);
while (0 < n) {
if ((n & 1) != 0) r = barrett.Mul(r, y);
y = barrett.Mul(y, y);
n >>= 1;
}
return r;
}
public static long SafeMod(long x, long m)
{
x %= m;
if (x < 0) x += m;
return x;
}
/// <summary>
/// g=gcd(a,b),xa=g(mod b) となるような 0≤x<b/g の(g, x)
/// </summary>
/// <remarks>
/// <para>制約: 1≤<paramref name="b"/></para>
/// </remarks>
public static (long, long) InvGCD(long a, long b)
{
a = SafeMod(a, b);
if (a == 0) return (b, 0);
long s = b, t = a;
long m0 = 0, 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;
}
}
/// <summary>
/// <paramref name="n"/> ≤ 2**x を満たす最小のx
/// </summary>
/// <remarks>
/// <para>制約: 0≤<paramref name="n"/></para>
/// </remarks>
public 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;
}
}
/// <summary>
/// Fast moduler by barrett reduction
/// <seealso href="https://en.wikipedia.org/wiki/Barrett_reduction"/>
/// </summary>
public class Barrett
{
public uint Mod { get; private set; }
private ulong IM;
public Barrett(uint m)
{
Mod = m;
IM = unchecked((ulong)-1) / m + 1;
}
/// <summary>
/// <paramref name="a"/> * <paramref name="b"/> mod m
/// </summary>
public uint Mul(uint a, uint b)
{
ulong z = a;
z *= b;
return (uint)(z % Mod);
}
}
public static class Butterfly<T> where T : struct, IStaticMod
{
/// <summary>
/// sumE[i] = ies[0] * ... * ies[i - 1] * es[i]
/// </summary>
private static StaticModInt<T>[] sumE = CalcurateSumE();
/// <summary>
/// sumIE[i] = es[0] * ... * es[i - 1] * ies[i]
/// </summary>
private static StaticModInt<T>[] sumIE = CalcurateSumIE();
public static void Calculate(Span<StaticModInt<T>> a)
{
var n = a.Length;
var h = InternalMath.CeilPow2(n);
for (int ph = 1; ph <= h; ph++) {
// ブロックサイズの半分
int w = 1 << (ph - 1);
// ブロック数
int p = 1 << (h - ph);
var now = StaticModInt<T>.Raw(1);
// 各ブロックの s 段目
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[InternalBit.BSF(~(uint)s)];
}
}
}
public static void CalculateInv(Span<StaticModInt<T>> a)
{
var n = a.Length;
var h = InternalMath.CeilPow2(n);
for (int ph = h; ph >= 1; ph--) {
// ブロックサイズの半分
int w = 1 << (ph - 1);
// ブロック数
int p = 1 << (h - ph);
var iNow = StaticModInt<T>.Raw(1);
// 各ブロックの s 段目
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] = StaticModInt<T>.Raw(
unchecked((int)((ulong)(default(T).Mod + l.Value - r.Value) * (ulong)iNow.Value % default(T).Mod)));
}
iNow *= sumIE[InternalBit.BSF(~(uint)s)];
}
}
}
private static StaticModInt<T>[] CalcurateSumE()
{
int g = InternalMath.PrimitiveRoot((int)default(T).Mod);
int cnt2 = InternalBit.BSF(default(T).Mod - 1);
var e = new StaticModInt<T>(g).Pow((default(T).Mod - 1) >> cnt2);
var ie = e.Inv();
var sumE = new StaticModInt<T>[cnt2 - 2];
// es[i]^(2^(2+i)) == 1
Span<StaticModInt<T>> es = stackalloc StaticModInt<T>[cnt2 - 1];
Span<StaticModInt<T>> ies = stackalloc StaticModInt<T>[cnt2 - 1];
for (int i = es.Length - 1; i >= 0; i--) {
// e^(2^(2+i)) == 1
es[i] = e;
ies[i] = ie;
e *= e;
ie *= ie;
}
var now = StaticModInt<T>.Raw(1);
for (int i = 0; i < sumE.Length; i++) {
sumE[i] = es[i] * now;
now *= ies[i];
}
return sumE;
}
private static StaticModInt<T>[] CalcurateSumIE()
{
int g = InternalMath.PrimitiveRoot((int)default(T).Mod);
int cnt2 = InternalBit.BSF(default(T).Mod - 1);
var e = new StaticModInt<T>(g).Pow((default(T).Mod - 1) >> cnt2);
var ie = e.Inv();
var sumIE = new StaticModInt<T>[cnt2 - 2];
// es[i]^(2^(2+i)) == 1
Span<StaticModInt<T>> es = stackalloc StaticModInt<T>[cnt2 - 1];
Span<StaticModInt<T>> ies = stackalloc StaticModInt<T>[cnt2 - 1];
for (int i = es.Length - 1; i >= 0; i--) {
// e^(2^(2+i)) == 1
es[i] = e;
ies[i] = ie;
e *= e;
ie *= ie;
}
var now = StaticModInt<T>.Raw(1);
for (int i = 0; i < sumIE.Length; i++) {
sumIE[i] = ies[i] * now;
now *= es[i];
}
return sumIE;
}
}
public static class InternalBit
{
/// <summary>
/// _blsi_u32 OR <paramref name="n"/> & -<paramref name="n"/>
/// <para><paramref name="n"/>で立っているうちの最下位の 1 ビットのみを立てた整数を返す</para>
/// </summary>
/// <param name="n"></param>
/// <returns><paramref name="n"/> & -<paramref name="n"/></returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int ExtractLowestSetBit(int n)
{
return n & -n;
}
/// <summary>
/// (<paramref name="n"/> & (1 << x)) != 0 なる最小の非負整数 x を求めます。
/// </summary>
/// <remarks>
/// <para>BSF: Bit Scan Forward</para>
/// <para>制約: 1 ≤ <paramref name="n"/></para>
/// </remarks>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int BSF(uint n)
{
for (int i = 0; i < 32; i++) {
if (((1 << i) & n) != 0) {
return i;
}
}
return 32;
}
}
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 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 int PopCount => (int)Popcnt.PopCount((uint)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 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);
}
}
}