結果

問題 No.2839 AND Constraint
ユーザー KumaTachiRen
提出日時 2024-08-09 22:19:47
言語 C#
(.NET 8.0.404)
結果
AC  
実行時間 118 ms / 2,000 ms
コード長 27,032 bytes
コンパイル時間 8,685 ms
コンパイル使用メモリ 168,472 KB
実行使用メモリ 192,264 KB
最終ジャッジ日時 2024-08-09 22:19:59
合計ジャッジ時間 10,911 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 16
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コンパイルメッセージ
  復元対象のプロジェクトを決定しています...
  /home/judge/data/code/main.csproj を復元しました (87 ms)。
MSBuild のバージョン 17.9.6+a4ecab324 (.NET)
/home/judge/data/code/Main.cs(83,3674): warning CS8632: '#nullable' 注釈コンテキスト内のコードでのみ、Null 許容参照型の注釈を使用する必要があります。 [/home/judge/data/code/main.csproj]
  main -> /home/judge/data/code/bin/Release/net8.0/main.dll
  main -> /home/judge/data/code/bin/Release/net8.0/publish/

ソースコード

diff #
プレゼンテーションモードにする

using Lib;
using Lib.MathLib;
using ModInt = Lib.StaticModInt<Lib.Mod998244353>;
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Text;
using static Lib.OutputLib;
public class Solver
{
    const bool MultiTestCase = false;
    void Solve()
    {
        int n = ri, m = ri;
        if (n <= 15 && (1 << n) - 1 < m)
        {
            Write(0);
            return;
        }
        var f = new ModInt[n + 1][];
        f[0] = new ModInt[m + 1];
        f[0][0] = 1;
        for (int x = 0; x < n; x++)
        {
            var g = new ModInt[m + 1];
            for (int y = 0; y <= m; y++) g[y] += f[x][y];
            for (int y = 1; y <= m; y++) g[y] += f[x][y - 1];
            var h = Convolution.Square<Mod998244353>(f[x]);
            for (int y = 1; y <= m; y++) g[y] += h[y - 1] - f[x][0] * f[x][y - 1];
            f[x + 1] = g;
        }
        Write(f[n][m]);
    }
#pragma warning disable CS0162
    public Solver() { if (!MultiTestCase) Solve(); else for (int t = ri; t > 0; t--) Solve(); }
#pragma warning restore CS0162
    const int IINF = 1 << 30;
    const long INF = 1L << 60;
    int ri { [MethodImpl(256)] get => (int)sc.Integer(); }
    long rl { [MethodImpl(256)] get => sc.Integer(); }
    uint rui { [MethodImpl(256)] get => (uint)sc.UInteger(); }
    ulong rul { [MethodImpl(256)] get => sc.UInteger(); }
    double rd { [MethodImpl(256)] get => sc.Double(); }
    string rs { [MethodImpl(256)] get => sc.Scan(); }
    string rline { [MethodImpl(256)] get => sc.Line(); }
    public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());
    void ReadArray(out int[] a, int n) { a = new int[n]; for (int i = 0; i < a.Length; i++) a[i] = ri; }
    void ReadArray(out long[] a, int n) { a = new long[n]; for (int i = 0; i < a.Length; i++) a[i] = rl; }
    void ReadArray<T>(out T[] a, int n, Func<T> read) { a = new T[n]; for (int i = 0; i < a.Length; i++) a[i] = read(); }
    void ReadArray<T>(out T[] a, int n, Func<int, T> read) { a = new T[n]; for (int i = 0; i < a.Length; i++) a[i] = read(i); }
}
static class Program
{
    static public void Main(string[] args)
    {
        SourceExpander.Expander.Expand();
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver();
        Console.Out.Flush();
    }
}
#region Expanded by https://github.com/kzrnm/SourceExpander
namespace Lib{public static class InternalBit{[MethodImpl(256)]public static uint ExtractLowestSetBit(int n){if(System.Runtime.Intrinsics.X86.Bmi1
    .IsSupported)return System.Runtime.Intrinsics.X86.Bmi1.ExtractLowestSetBit((uint)n);return(uint)(n&-n);}[MethodImpl(256)]public static int Bsf
    (uint n){return BitOperations.TrailingZeroCount(n);}[MethodImpl(256)]public static int CeilPow2(int n){var un=(uint)n;if(un<=1)return 0;return 
    BitOperations.Log2(un-1)+1;}}}
namespace Lib{public partial class StreamScanner{public int[][]ReadUnweightedTree(int n,int origin=1){var gr=new List<int>[n];for(int i=0;i<n;i
    ++)gr[i]=new List<int>();for(int i=0;i<n-1;i++){int u=(int)(Integer()-origin);int v=(int)(Integer()-origin);gr[u].Add(v);gr[v].Add(u);}var g=new 
    int[n][];for(int i=0;i<n;i++)g[i]=gr[i].ToArray();return g;}}}
namespace Lib{public partial class StreamScanner{public StreamScanner(Stream stream){str=stream;}private readonly Stream str;private readonly 
    byte[]buf=new byte[1024];private int len,ptr;public bool isEof=false;public bool IsEndOfStream{get{return isEof;}}[MethodImpl(256)]private byte 
    Read(){if(isEof)throw new EndOfStreamException();if(ptr>=len){ptr=0;if((len=str.Read(buf,0,1024))<=0){isEof=true;return 0;}}return buf[ptr++]
    ;}[MethodImpl(256)]public char Char(){byte b=0;do b=Read();while(b<33||126<b);return(char)b;}[MethodImpl(256)]public string Line(){var sb=new 
    StringBuilder();for(var b=Char();b!=10&&!isEof;b=(char)Read())sb.Append(b);return sb.ToString();}[MethodImpl(256)]public string Scan(){var sb=new 
    StringBuilder();for(var b=Char();b>=33&&b<=126;b=(char)Read())sb.Append(b);return sb.ToString();}[MethodImpl(256)]public long Integer(){long ret=0
    ;byte b=0;var 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(256)]public ulong UInteger(){ulong ret=0;byte b=0;do b=Read();while(b<'0'||'9'<b);for(;true;b=Read()){if
    (b<'0'||'9'<b)return ret;else ret=ret*10+b-'0';}}[MethodImpl(256)]public double Double()=>double.Parse(Scan());}}
namespace Lib.MathLib{public static class Convolution{[MethodImpl(256)]public static long[]Calc<TMod>(ReadOnlySpan<long>a,ReadOnlySpan<long>b)where 
    TMod:struct,IStaticMod{var u=new StaticModInt<TMod>[a.Length];for(int i=0;i<a.Length;i++)u[i]=a[i];var v=new StaticModInt<TMod>[b.Length];for(int 
    i=0;i<b.Length;i++)v[i]=b[i];u=Calc<TMod>(u,v);var r=new long[u.Length];for(int i=0;i<u.Length;i++)r[i]=u[i];return r;}[MethodImpl(256)]public 
    static StaticModInt<TMod>[]Calc<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(Math.Min(n,m)<=30)return Naive(a,b);return FFT(a,b);}[MethodImpl
    (256)]public static StaticModInt<TMod>[]Calc<TMod>(StaticModInt<TMod>[]a,StaticModInt<TMod>[]b)where TMod:struct,IStaticMod=>Calc((ReadOnlySpan
    <StaticModInt<TMod>>)a,b);[MethodImpl(256)]public static StaticModInt<TMod>[]Square<TMod>(ReadOnlySpan<StaticModInt<TMod>>a)where TMod:struct
    ,IStaticMod{var n=a.Length;if(n==0)return Array.Empty<StaticModInt<TMod>>();if(n<=30)return Naive(a,a);return SquareFFT(a);}[MethodImpl(256
    )]private static StaticModInt<TMod>[]SquareFFT<TMod>(ReadOnlySpan<StaticModInt<TMod>>a)where TMod:struct,IStaticMod{int n=a.Length;int z=1
    <<InternalBit.CeilPow2(2*n-1);var a2=new StaticModInt<TMod>[z];a.CopyTo(a2);Butterfly<TMod>.Calculate(a2);for(int i=0;i<a2.Length;i++)a2[i]*=a2[i]
    ;Butterfly<TMod>.CalculateInv(a2);Array.Resize(ref a2,2*n-1);var iz=new StaticModInt<TMod>(z).Inv();for(int i=0;i<a2.Length;i++)a2[i]*=iz;return 
    a2;}[MethodImpl(256)]private static StaticModInt<TMod>[]FFT<TMod>(ReadOnlySpan<StaticModInt<TMod>>a,ReadOnlySpan<StaticModInt<TMod>>b)where TMod
    :struct,IStaticMod{int n=a.Length,m=b.Length;int z=1<<InternalBit.CeilPow2(n+m-1);var a2=new StaticModInt<TMod>[z];var b2=new StaticModInt<TMod
    >[z];a.CopyTo(a2);b.CopyTo(b2);var result=FFTInner(a2,b2);Array.Resize(ref result,n+m-1);var iz=new StaticModInt<TMod>(z).Inv();for(int i=0;i
    <result.Length;i++)result[i]*=iz;return result;}[MethodImpl(256)]private static StaticModInt<TMod>[]FFTInner<TMod>(StaticModInt<TMod>[]a
    ,StaticModInt<TMod>[]b)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);return a;}[MethodImpl(256)]private static StaticModInt<TMod>[]Naive<TMod>(ReadOnlySpan<StaticModInt<TMod>>a
    ,ReadOnlySpan<StaticModInt<TMod>>b)where TMod:struct,IStaticMod{if(a.Length<b.Length){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;}[MethodImpl(256)]public static 
    long[]Long(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;const ulong M1M2M3=Mod1*Mod2*Mod3;const ulong i1=190329765;const ulong i2=58587104;const ulong i3=187290749;var c1=Calc<FFTMod1>(a,b);var c2
    =Calc<FFTMod2>(a,b);var c3=Calc<FFTMod3>(a,b);var c=new long[n+m-1];for(int i=0;i<c.Length;i++){ulong x=0;x+=((ulong)c1[i]*i1)%Mod1*M2M3;x
    +=((ulong)c2[i]*i2)%Mod2*M1M3;x+=((ulong)c3[i]*i3)%Mod3*M1M2;long diff=c1[i]-InternalMath.SafeMod((long)x,(long)Mod1);if(diff<0)diff+=(long)Mod1
    ;switch(diff%5){case 2:x-=M1M2M3;break;case 3:x-=2*M1M2M3;break;case 4:x-=3*M1M2M3;break;}c[i]=(long)x;}return c;}}[MethodImpl(256)]public static 
    StaticModInt<Mod>[]IntMod<Mod>(ReadOnlySpan<StaticModInt<Mod>>a,ReadOnlySpan<StaticModInt<Mod>>b)where Mod:struct,IStaticMod{var n=a.Length;var m
    =b.Length;if(n==0||m==0)return Array.Empty<StaticModInt<Mod>>();const long Mod1=754974721;const long Mod2=167772161;const long Mod3=469762049
    ;const long M1invM2=95869806;const long M12invM3=187290749;int mod=StaticModInt<Mod>.Mod;long M12mod=Mod1*Mod2%mod;var u=new long[n];for(int i=0;i
    <n;i++)u[i]=a[i];var v=new long[m];for(int i=0;i<m;i++)v[i]=b[i];var c1=Calc<FFTMod1>(u,v);var c2=Calc<FFTMod2>(u,v);var c3=Calc<FFTMod3>(u,v);var 
    c=new StaticModInt<Mod>[n+m-1];for(int i=0;i<c.Length;i++){long v1=(c2[i]-c1[i])*M1invM2%Mod2;if(v1<0)v1+=Mod2;long v2=(c3[i]-(c1[i]+Mod1*v1)%Mod3
    )*M12invM3%Mod3;if(v2<0)v2+=Mod3;long v3=(c1[i]+Mod1*v1+M12mod*v2)%mod;if(v3<0)v3+=mod;c[i]=v3;}return c;}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;}}}
namespace Lib{public class Barrett{public readonly uint Mod;public readonly ulong IM;public Barrett(uint m){Mod=m;IM=unchecked((ulong)-1)/m+1
    ;}[MethodImpl(256)]public uint Mul(uint a,uint b)=>Reduce((ulong)a*b);[MethodImpl(256)]public uint Reduce(ulong z){var x=InternalMath.Mul128Bit(z
    ,IM);var v=unchecked((uint)(z-x*Mod));if(Mod<=v)v+=Mod;return v;}[MethodImpl(256)]public uint Pow(long x,long n){if(Mod==1)return 0;uint r=1,y
    =(uint)InternalMath.SafeMod(x,Mod);while(n>0){if((n&1)!=0)r=Mul(r,y);y=Mul(y,y);n>>=1;}return r;}}}
namespace Lib{public static class Butterfly{public static uint Mod{get;private set;}public static uint[]sumE;public static uint[]sumIE;public static 
    void SetMod(uint mod){Mod=mod;Montgomery.Init(mod);sumE=CalcurateSumE();sumIE=CalcurateSumIE();}[MethodImpl(256)]public static void Calculate(Span
    <uint>a){var n=a.Length;var h=InternalBit.CeilPow2(n);var regLength=Vector<uint>.Count;var modV=new Vector<uint>(Mod);for(int ph=1;ph<=h;ph++){int 
    w=1<<(ph-1);int p=1<<(h-ph);uint now=1;for(int s=0;s<w;s++){int offset=s<<(h-ph+1);var ls=a.Slice(offset,p);var rs=a.Slice(offset+p,p);if(p
    <regLength){for(int i=0;i<p;i++){var l=ls[i];var r=Montgomery.Mul(rs[i],now);ls[i]=l+r;if(ls[i]>=Mod)ls[i]-=Mod;rs[i]=l-r;if(rs[i]>=Mod)rs[i]+=Mod
    ;}}else{foreach(ref var r in rs)r=Montgomery.Mul(r,now);for(int i=0;i<ls.Length;i+=regLength){var lsSliced=ls.Slice(i);var rsSliced=rs.Slice(i
    );var u=new Vector<uint>(lsSliced);var v=new Vector<uint>(rsSliced);var add=u+v;var sub=u-v;var ge=Vector.GreaterThanOrEqual(add,modV);add=Vector
    .ConditionalSelect(ge,add-modV,add);ge=Vector.GreaterThanOrEqual(sub,modV);sub=Vector.ConditionalSelect(ge,sub+modV,sub);add.CopyTo(lsSliced);sub
    .CopyTo(rsSliced);}}now=Montgomery.Mul(now,sumE[InternalBit.Bsf(~(uint)s)]);}}}[MethodImpl(256)]public static void CalculateInv(Span<uint>a){var n
    =a.Length;var h=InternalBit.CeilPow2(n);var regLength=Vector<uint>.Count;var modV=new Vector<uint>(Mod);for(int ph=h;ph>=1;ph--){int w=1<<(ph-1
    );int p=1<<(h-ph);uint iNow=1;for(int s=0;s<w;s++){int offset=s<<(h-ph+1);var ls=a.Slice(offset,p);var rs=a.Slice(offset+p,p);if(p<regLength){for
    (int i=0;i<p;i++){var l=ls[i];var r=rs[i];ls[i]=l+r;if(ls[i]>=Mod)ls[i]-=Mod;rs[i]=l-r;if(rs[i]>=Mod)rs[i]+=Mod;rs[i]=Montgomery.Mul(rs[i],iNow
    );}}else{for(int i=0;i<ls.Length;i+=regLength){var lsSliced=ls.Slice(i);var rsSliced=rs.Slice(i);var u=new Vector<uint>(lsSliced);var v=new Vector
    <uint>(rsSliced);var add=u+v;var sub=u-v;var ge=Vector.GreaterThanOrEqual(add,modV);add=Vector.ConditionalSelect(ge,add-modV,add);sub+=modV;add
    .CopyTo(lsSliced);sub.CopyTo(rsSliced);}foreach(ref var r in rs)r=Montgomery.Mul(r,iNow);}iNow=Montgomery.Mul(iNow,sumIE[InternalBit.Bsf(~(uint)s
    )]);}}}public static uint[]CalcurateSumE(){uint g=(uint)InternalMath.PrimitiveRoot(Mod);int cnt2=InternalBit.Bsf(Mod-1);var e=Pow(g,(Mod-1)>>cnt2
    );var ie=Pow(e,Mod-2);var sumE=new uint[30];Span<uint>es=stackalloc uint[cnt2-1];Span<uint>ies=stackalloc uint[cnt2-1];for(int i=es.Length-1;i>=0
    ;i--){es[i]=e;ies[i]=ie;e=Montgomery.Mul(e,e);ie=Montgomery.Mul(ie,ie);}uint now=1;for(int i=0;i<=cnt2-2;i++){sumE[i]=Montgomery.Mul(es[i],now
    );now=Montgomery.Mul(now,ies[i]);}return sumE;}public static uint[]CalcurateSumIE(){uint g=(uint)InternalMath.PrimitiveRoot(Mod);int cnt2
    =InternalBit.Bsf(Mod-1);var e=Pow(g,(Mod-1)>>cnt2);var ie=Pow(e,Mod-2);var sumIE=new uint[30];Span<uint>es=stackalloc uint[cnt2-1];Span<uint>ies
    =stackalloc uint[cnt2-1];for(int i=es.Length-1;i>=0;i--){es[i]=e;ies[i]=ie;e=Montgomery.Mul(e,e);ie=Montgomery.Mul(ie,ie);}uint now=1;for(int i=0
    ;i<=cnt2-2;i++){sumIE[i]=Montgomery.Mul(ies[i],now);now=Montgomery.Mul(now,es[i]);}return sumIE;}static uint Pow(uint x,uint n){uint y=1;for(;n>0
    ;n>>=1){if((n&1)==1)y=Montgomery.Mul(y,x);x=Montgomery.Mul(x,x);}return y;}[Conditional("ATCODER_CONTRACT")]private static void CheckPow2(int n
    ){if(BitOperations.PopCount((uint)n)!=1){throw new ArgumentException("配列長は2のべき乗でなければなりません。");}}}public static class Butterfly<T
    >where T:struct,IStaticMod{public static readonly StaticModInt<T>[]sumE=CalcurateSumE();public static readonly StaticModInt<T>[]sumIE
    =CalcurateSumIE();[MethodImpl(256)]public static void Calculate(Span<StaticModInt<T>>a){var n=a.Length;var h=InternalBit.CeilPow2(n);var regLength
    =Vector<uint>.Count;var modV=new Vector<uint>(default(T).Mod);for(int ph=1;ph<=h;ph++){int w=1<<(ph-1);int p=1<<(h-ph);var now=StaticModInt<T>.Raw
    (1);for(int s=0;s<w;s++){int offset=s<<(h-ph+1);var ls=a.Slice(offset,p);var rs=a.Slice(offset+p,p);if(p<regLength){for(int i=0;i<p;i++){var l
    =ls[i];var r=rs[i]*now;ls[i]=l+r;rs[i]=l-r;}}else{foreach(ref var r in rs){r*=now;}var lu=MemoryMarshal.Cast<StaticModInt<T>,uint>(ls);var ru
    =MemoryMarshal.Cast<StaticModInt<T>,uint>(rs);for(int i=0;i<lu.Length;i+=regLength){var luSliced=lu.Slice(i);var ruSliced=ru.Slice(i);var u=new 
    Vector<uint>(luSliced);var v=new Vector<uint>(ruSliced);var add=u+v;var sub=u-v;var ge=Vector.GreaterThanOrEqual(add,modV);add=Vector
    .ConditionalSelect(ge,add-modV,add);ge=Vector.GreaterThanOrEqual(sub,modV);sub=Vector.ConditionalSelect(ge,sub+modV,sub);add.CopyTo(luSliced);sub
    .CopyTo(ruSliced);}}now*=sumE[InternalBit.Bsf(~(uint)s)];}}}[MethodImpl(256)]public static void CalculateInv(Span<StaticModInt<T>>a){var n=a
    .Length;var h=InternalBit.CeilPow2(n);var regLength=Vector<uint>.Count;var modV=new Vector<uint>(default(T).Mod);for(int ph=h;ph>=1;ph--){int w=1
    <<(ph-1);int p=1<<(h-ph);var iNow=StaticModInt<T>.Raw(1);for(int s=0;s<w;s++){int offset=s<<(h-ph+1);var ls=a.Slice(offset,p);var rs=a.Slice
    (offset+p,p);if(p<regLength){for(int i=0;i<p;i++){var l=ls[i];var r=rs[i];ls[i]=l+r;rs[i]=StaticModInt<T>.Raw((int)((ulong)(default(T).Mod+l.Value
    -r.Value)*(ulong)iNow.Value%default(T).Mod));}}else{var lu=MemoryMarshal.Cast<StaticModInt<T>,uint>(ls);var ru=MemoryMarshal.Cast<StaticModInt<T
    >,uint>(rs);for(int i=0;i<lu.Length;i+=regLength){var luSliced=lu.Slice(i);var ruSliced=ru.Slice(i);var u=new Vector<uint>(luSliced);var v=new 
    Vector<uint>(ruSliced);var add=u+v;var sub=u-v;var ge=Vector.GreaterThanOrEqual(add,modV);add=Vector.ConditionalSelect(ge,add-modV,add);sub+=modV
    ;add.CopyTo(luSliced);sub.CopyTo(ruSliced);}foreach(ref var r in rs){r*=iNow;}}iNow*=sumIE[InternalBit.Bsf(~(uint)s)];}}}public static 
    StaticModInt<T>[]CalcurateSumE(){int g=InternalMath.PrimitiveRoot<T>();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>[30];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--){es[i]=e;ies[i]=ie;e*=e;ie*=ie;}var now=StaticModInt<T>.Raw
    (1);for(int i=0;i<=cnt2-2;i++){sumE[i]=es[i]*now;now*=ies[i];}return sumE;}public static StaticModInt<T>[]CalcurateSumIE(){int g=InternalMath
    .PrimitiveRoot<T>();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>[30];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--){es[i]=e;ies[i]=ie;e*=e;ie*=ie;}var now=StaticModInt<T>.Raw(1);for(int i=0;i<=cnt2-2;i++){sumIE[i]=ies[i]*now;now
    *=es[i];}return sumIE;}[Conditional("ATCODER_CONTRACT")]private static void CheckPow2(int n){if(BitOperations.PopCount((uint)n)!=1){throw new 
    ArgumentException("配列長は2のべき乗でなければなりません。");}}}}
namespace Lib{public static class InternalMath{private static readonly Dictionary<uint,int>primitiveRootsCache=new Dictionary<uint,int>(){{2,1}
    ,{167772161,3},{469762049,3},{754974721,11},{998244353,3}};[MethodImpl(256)]public static int PrimitiveRoot<TMod>()where TMod:struct
    ,IStaticMod{uint m=default(TMod).Mod;if(primitiveRootsCache.TryGetValue(m,out var p))return p;return primitiveRootsCache[m]=PrimitiveRootCalculate
    <TMod>();}static int PrimitiveRootCalculate<TMod>()where TMod:struct,IStaticMod{var m=default(TMod).Mod;Span<uint>divs=stackalloc uint[20];divs[0]
    =2;int cnt=1;var x=m-1;x>>=BitOperations.TrailingZeroCount(x);for(uint i=3;(long)i*i<=x;i+=2){if(x%i==0){divs[cnt++]=i;do{x/=i;}while(x%i==0);}}if
    (x>1){divs[cnt++]=x;}divs=divs.Slice(0,cnt);for(int g=2;;g++){foreach(var d in divs)if(new StaticModInt<TMod>(g).Pow((m-1)/d).Value==1)goto NEXT
    ;return g;NEXT:;}}[MethodImpl(256)]public static int PrimitiveRoot(uint m){if(primitiveRootsCache.TryGetValue(m,out var p))return p;return 
    primitiveRootsCache[m]=PrimitiveRootCalculate(m);}static int PrimitiveRootCalculate(uint m){Span<uint>divs=stackalloc uint[20];divs[0]=2;int cnt=1
    ;var x=m-1;x>>=BitOperations.TrailingZeroCount(x);for(uint i=3;(long)i*i<=x;i+=2){if(x%i==0){divs[cnt++]=i;do{x/=i;}while(x%i==0);}}if(x>1
    ){divs[cnt++]=x;}divs=divs.Slice(0,cnt);uint Pow(uint x,uint n){uint y=1;while(n>0){if((n&1)==1)y=y*x%m;x=x*x%m;n/=2;}return y;}for(uint g=2;;g
    ++){foreach(var d in divs)if(Pow(g,(m-1)/d)==1)goto NEXT;return(int)g;NEXT:;}}[MethodImpl(256)]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;}}[MethodImpl(256)]public static long SafeMod(long x,long m){x%=m;if(x<0)x+=m;return x
    ;}[MethodImpl(256)]public static bool IsPrime(int n){if(n<=1)return false;if(n==2||n==7||n==61)return true;if(n%2==0)return false;long d=n-1;while
    (d%2==0)d/=2;ReadOnlySpan<byte>bases=stackalloc byte[3]{2,7,61};foreach(long a in bases){long t=d;long y=PowMod(a,t,n);while(t!=n-1&&y!=1&&y!=n-1
    ){y=y*y%n;t<<=1;}if(y!=n-1&&t%2==0){return false;}}return true;}[MethodImpl(256)]public static uint PowMod(long x,long n,int m){if(m==1)return 0
    ;return new Barrett((uint)m).Pow(x,n);}[MethodImpl(256)]public static uint PowMod(long x,long n,uint m){if(m==1)return 0;return new Barrett(m).Pow
    (x,n);}[MethodImpl(256)]public static ulong FloorSumUnsigned(ulong n,ulong m,ulong a,ulong b){ulong ans=0;while(true){if(a>=m){ans+=(n-1)*n/2*(a/m
    );a%=m;}if(b>=m){ans+=n*(b/m);b%=m;}ulong yMax=a*n+b;if(yMax<m)return ans;(n,m,a,b)=(yMax/m,a,m,yMax%m);}}[MethodImpl(256)]public static ulong 
    Mul128Bit(ulong a,ulong b){if(System.Runtime.Intrinsics.X86.Bmi2.X64.IsSupported)return System.Runtime.Intrinsics.X86.Bmi2.X64.MultiplyNoFlags(a,b
    );return Mul128BitLogic(a,b);}[MethodImpl(256)]internal static ulong Mul128BitLogic(ulong a,ulong b){var au=a>>32;var ad=a&0xFFFFFFFF;var bu=b>>32
    ;var bd=b&0xFFFFFFFF;var l=ad*bd;var m1=au*bd;var m2=ad*bu;var h=au*bu;var lu=l>>32;var m1d=m1&0xFFFFFFFF;var m2d=m2&0xFFFFFFFF;var c=m1d+m2d+lu
    ;return h+(m1>>32)+(m2>>32)+(c>>32);}}}
namespace Lib{public interface IStaticMod{uint Mod{get;}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;}public readonly 
    struct StaticModInt<T>:IEquatable<StaticModInt<T>>where T:struct,IStaticMod{internal readonly uint _v;private static readonly T op=default;public 
    int Value=>(int)_v;public static int Mod=>(int)op.Mod;public static StaticModInt<T>Zero=>default;public static StaticModInt<T>One=>new 
    StaticModInt<T>(1u);[MethodImpl(256)]public static StaticModInt<T>Raw(int v){var u=unchecked((uint)v);return new StaticModInt<T>(u);}[MethodImpl
    (256)]public StaticModInt(long v):this(Round(v)){}[MethodImpl(256)]public StaticModInt(ulong v):this((uint)(v%op.Mod)){}[MethodImpl(256)]private 
    StaticModInt(uint v)=>_v=v;[MethodImpl(256)]private static uint Round(long v){var x=v%op.Mod;if(x<0)x+=op.Mod;return(uint)x;}[MethodImpl(256
    )]public static StaticModInt<T>operator ++(StaticModInt<T>v){var x=v._v+1;if(x==op.Mod)x=0;return new StaticModInt<T>(x);}[MethodImpl(256)]public 
    static StaticModInt<T>operator --(StaticModInt<T>v){var x=v._v;if(x==0)x=op.Mod;return new StaticModInt<T>(x-1);}[MethodImpl(256)]public static 
    StaticModInt<T>operator+(StaticModInt<T>lhs,StaticModInt<T>rhs){var v=lhs._v+rhs._v;if(v>=op.Mod)v-=op.Mod;return new StaticModInt<T>(v
    );}[MethodImpl(256)]public static StaticModInt<T>operator-(StaticModInt<T>lhs,StaticModInt<T>rhs){unchecked{var v=lhs._v-rhs._v;if(v>=op.Mod)v+=op
    .Mod;return new StaticModInt<T>(v);}}[MethodImpl(256)]public static StaticModInt<T>operator*(StaticModInt<T>lhs,StaticModInt<T>rhs)=>new 
    StaticModInt<T>((uint)((ulong)lhs._v*rhs._v%op.Mod));[MethodImpl(256)]public static StaticModInt<T>operator/(StaticModInt<T>lhs,StaticModInt<T>rhs
    )=>new StaticModInt<T>((uint)((ulong)lhs._v*Inv(rhs._v)%op.Mod));[MethodImpl(256)]public static StaticModInt<T>operator+(StaticModInt<T>v)=>v
    ;[MethodImpl(256)]public static StaticModInt<T>operator-(StaticModInt<T>v)=>new StaticModInt<T>(v._v==0?0:op.Mod-v._v);[MethodImpl(256)]public 
    static bool operator==(StaticModInt<T>lhs,StaticModInt<T>rhs)=>lhs._v==rhs._v;[MethodImpl(256)]public static bool operator!=(StaticModInt<T>lhs
    ,StaticModInt<T>rhs)=>lhs._v!=rhs._v;[MethodImpl(256)]public static implicit operator StaticModInt<T>(int v)=>new StaticModInt<T>(v);[MethodImpl
    (256)]public static implicit operator StaticModInt<T>(uint v)=>new StaticModInt<T>((long)v);[MethodImpl(256)]public static implicit operator 
    StaticModInt<T>(long v)=>new StaticModInt<T>(v);[MethodImpl(256)]public static implicit operator StaticModInt<T>(ulong v)=>new StaticModInt<T>(v
    );[MethodImpl(256)]public static implicit operator long(StaticModInt<T>v)=>v._v;[MethodImpl(256)]public static implicit operator ulong
    (StaticModInt<T>v)=>v._v;[MethodImpl(256)]public StaticModInt<T>Pow(long n){var x=this;var r=new StaticModInt<T>(1U);if(n<0)(x,n)=(x.Inv(),-n
    );while(n>0){if((n&1)>0)r*=x;x*=x;n>>=1;}return r;}[MethodImpl(256)]public StaticModInt<T>Inv()=>new StaticModInt<T>(Inv(_v));[MethodImpl(256
    )]static ulong Inv(ulong x){long u=op.Mod,xu=1,yu=0,v=(long)x,xv=0,yv=1;while(v!=0){long w=SafeMod(u,v);long q=(u-w)/v;long xw=xu-xv*q;long yw=yu
    -yv*q;u=v;xu=xv;yu=yv;v=w;xv=xw;yv=yw;}return(ulong)(yu<0?yu+op.Mod:yu);}[MethodImpl(256)]static long SafeMod(long x,long m){long r=x%m;if(r<0)r
    +=m;return r;}[MethodImpl(256)]public override string ToString()=>_v.ToString();[MethodImpl(256)]public string ToString(string format
    ,IFormatProvider formatProvider)=>_v.ToString(format,formatProvider);[MethodImpl(256)]public override bool Equals(object?obj)=>obj is StaticModInt
    <T>m&&Equals(m);[MethodImpl(256)]public bool Equals(StaticModInt<T>other)=>_v==other._v;[MethodImpl(256)]public override int GetHashCode()=>_v
    .GetHashCode();}}
public static class Montgomery{public static uint MOD{get;private set;}const int L=31;const ulong mask=(1UL<<L)-1;static ulong r2,nr;public static 
    void Init(uint mod){if(MOD!=mod){MOD=mod;r2=(1UL<<(L<<1))%MOD;nr=0;ulong t=0,vi=1;for(int i=0;i<L;i++){if((t&1)==0){t+=MOD;nr+=vi;}t>>=1;vi<<=1
    ;}}}[MethodImpl(256)]public static ulong Reduction(ulong t){ulong c=t*nr;c&=mask;c*=MOD;c+=t;c>>=L;if(c>=MOD)c-=MOD;return c;}[MethodImpl(256
    )]public static ulong Transform(ulong t)=>Reduction(t*r2);[MethodImpl(256)]public static ulong Mul(ulong a,ulong b)=>Reduction(Reduction(a*b)*r2
    );[MethodImpl(256)]public static uint Mul(uint a,uint b)=>(uint)Mul((ulong)a,b);[MethodImpl(256)]public static long Mul(long a,long b)=>(long)Mul
    ((ulong)a,(ulong)b);[MethodImpl(256)]public static int Mul(int a,int b)=>(int)Mul((ulong)a,(ulong)b);[MethodImpl(256)]public static ulong Pow
    (ulong a,ulong b){ulong p=Transform(a),x=Transform(1);while(b>0){if((b&1)==1)x=Reduction(x*p);p=Reduction(p*p);b>>=1;}return Reduction(x);}}
namespace Lib{public static class OutputLib{[MethodImpl(256)]public static void WriteJoin<T>(string s,IEnumerable<T>t)=>Console.WriteLine(string.Join
    (s,t));[MethodImpl(256)]public static void WriteMat<T>(T[,]a,string sep=" "){int sz1=a.GetLength(0),sz2=a.GetLength(1);var b=new T[sz2];for(int i
    =0;i<sz1;i++){for(int j=0;j<sz2;j++)b[j]=a[i,j];WriteJoin(sep,b);}}[MethodImpl(256)]public static void WriteMat<T>(T[][]a,string sep=" "){for(int 
    i=0;i<a.Length;i++)WriteJoin(sep,a[i]);}[MethodImpl(256)]public static void WriteMat<T>(T[][]a,Func<T,string>map,string sep=" "){for(int i=0;i<a
    .Length;i++)WriteJoin(sep,a[i].Select(x=>map(x)));}[MethodImpl(256)]public static void Write(object t)=>Console.WriteLine(t.ToString
    ());[MethodImpl(256)]public static void Write(params object[]arg)=>Console.WriteLine(string.Join(" ",arg.Select(x=>x.ToString())));[MethodImpl(256
    )]public static void Write(string str)=>Console.WriteLine(str);[MethodImpl(256)]public static void WriteFlush(object t){Console.WriteLine(t
    .ToString());Console.Out.Flush();}[MethodImpl(256)]public static void WriteError(object t)=>Console.Error.WriteLine(t.ToString());[MethodImpl(256
    )]public static void Flush()=>Console.Out.Flush();[MethodImpl(256)]public static void YN(bool t)=>Console.WriteLine(t?"YES":"NO");[MethodImpl(256
    )]public static void Yn(bool t)=>Console.WriteLine(t?"Yes":"No");[MethodImpl(256)]public static void yn(bool t)=>Console.WriteLine(t?"yes":"no"
    );[MethodImpl(256)]public static void DeleteLine()=>Console.Write("\x1b[1A\x1b[2K");[MethodImpl(256)]public static void ProgressBar(long now,long 
    total,int blocks=50){int x=(int)((2*now*blocks+1)/(2*total));Console.Write($"\x1b[G[\x1b[42m{string.Concat(Enumerable.Repeat("_",x
    ))}\x1b[0m{string.Concat(Enumerable.Repeat("_",blocks-x))}] : {now} / {total}");}}}
namespace SourceExpander{public class Expander{[Conditional("EXP")]public static void Expand(string inputFilePath=null,string outputFilePath=null,bool 
    ignoreAnyError=true){}public static string ExpandString(string inputFilePath=null,bool ignoreAnyError=true){return "";}}}
#endregion Expanded by https://github.com/kzrnm/SourceExpander
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