#1008362 (C#) No.2883 K-powered Sum of Fibonacci

提出ソース

結果

問題	No.2883 K-powered Sum of Fibonacci
ユーザー	KumaTachiRen
提出日時	2024-09-08 13:03:19
言語	C# (.NET 8.0.203)
結果	AC
実行時間	104 ms / 3,000 ms
コード長	26,248 bytes
コンパイル時間	8,557 ms
コンパイル使用メモリ	167,212 KB
実行使用メモリ	193,132 KB
最終ジャッジ日時	2024-09-08 13:03:34
合計ジャッジ時間	13,019 ms
ジャッジサーバーID （参考情報）	judge5 / judge4

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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	44 ms 24,192 KB
testcase_01	AC	44 ms 23,672 KB
testcase_02	AC	43 ms 23,808 KB
testcase_03	AC	46 ms 23,808 KB
testcase_04	AC	46 ms 23,808 KB
testcase_05	AC	73 ms 26,452 KB
testcase_06	AC	45 ms 24,192 KB
testcase_07	AC	76 ms 27,008 KB
testcase_08	AC	72 ms 26,368 KB
testcase_09	AC	62 ms 26,112 KB
testcase_10	AC	74 ms 26,624 KB
testcase_11	AC	98 ms 29,952 KB
testcase_12	AC	75 ms 26,496 KB
testcase_13	AC	50 ms 24,192 KB
testcase_14	AC	96 ms 29,696 KB
testcase_15	AC	85 ms 26,880 KB
testcase_16	AC	45 ms 23,672 KB
testcase_17	AC	80 ms 26,624 KB
testcase_18	AC	51 ms 24,320 KB
testcase_19	AC	80 ms 26,752 KB
testcase_20	AC	104 ms 30,080 KB
testcase_21	AC	104 ms 30,080 KB
testcase_22	AC	101 ms 29,824 KB
testcase_23	AC	103 ms 29,652 KB
testcase_24	AC	99 ms 29,824 KB
testcase_25	AC	102 ms 29,696 KB
testcase_26	AC	102 ms 29,696 KB
testcase_27	AC	102 ms 29,824 KB
testcase_28	AC	102 ms 29,560 KB
testcase_29	AC	104 ms 29,560 KB
testcase_30	AC	62 ms 26,324 KB
testcase_31	AC	46 ms 23,808 KB
testcase_32	AC	43 ms 23,808 KB
testcase_33	AC	68 ms 26,324 KB
testcase_34	AC	44 ms 23,680 KB
testcase_35	AC	43 ms 23,936 KB
testcase_36	AC	46 ms 24,064 KB
testcase_37	AC	45 ms 23,936 KB
testcase_38	AC	46 ms 23,808 KB
testcase_39	AC	46 ms 23,672 KB
testcase_40	AC	45 ms 23,680 KB
testcase_41	AC	45 ms 23,892 KB
testcase_42	AC	104 ms 193,132 KB

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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 (95 ms)。
MSBuild のバージョン 17.9.6+a4ecab324 (.NET)
/home/judge/data/code/Main.cs(75,3674): 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

raw source code

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()
    {
        long n = rl;
        int k = ri;

        int m = (k + 1) * 4;
        var f = new ModInt[m];
        f[0] = 1;
        f[1] = 1;
        for (int i = 2; i < m; i++) f[i] = f[i - 1] + f[i - 2];
        var g = new ModInt[m + 1];
        for (int i = 0; i < m; i++) g[i + 1] = g[i] + f[i].Pow(k);

        var v = BerlekampMassey.Calc<Mod998244353>(g);
        var u = Convolution.Calc(v, g)[..m];
        Write(BostanMori<Mod998244353>.CalcConvolution(u, v, n));
    }

#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 uint[]Calc<TMod>(ReadOnlySpan<uint>a,ReadOnlySpan<uint>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 uint[u.Length];for(int i=0;i<u.Length;i++)r[i]=(uint)u[i].Value;return r;}[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 len=2*n-1;int z=1<<InternalBit.CeilPow2(len);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);var r=a2[..len];var iz=new StaticModInt<TMod>(z).Inv();foreach(ref var x in r.AsSpan())x*=iz;return r;}[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 len=n+m-1;int z=1<<InternalBit.CeilPow2(len);var a2=new StaticModInt<TMod>[z];var b2=new StaticModInt<TMod>[z];a.CopyTo(a2);b.CopyTo(b2);Butterfly<TMod>.Calculate(a2);Butterfly<TMod>.Calculate(b2);for(int i=0;i<a2.Length;i++)a2[i]*=b2[i];Butterfly<TMod>.CalculateInv(a2);var r=a2[..len];var iz=new StaticModInt<TMod>(z).Inv();foreach(ref var x in r.AsSpan())x*=iz;return r;}[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<T>where T:struct,IStaticMod{public static readonly StaticModInt<T>[]sumE=CalcurateSumE();public static readonly StaticModInt<T>[]sumIE=CalcurateSumIE();public static readonly uint Mod=default(T).Mod;[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>(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>(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)(Mod+l.Value-r.Value)*(ulong)iNow.Value%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("Array length must be a power of 2.");}}}}
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.MathLib{public static class BerlekampMassey{public static StaticModInt<Mod>[]Calc<Mod>(ReadOnlySpan<StaticModInt<Mod>>s)where Mod:struct,IStaticMod{int n=s.Length;var b=new StaticModInt<Mod>[n+1];var c=new StaticModInt<Mod>[n+1];b[0]=1;c[0]=1;int lb=1,lc=1;StaticModInt<Mod>y=1;for(int k=0;k<n;k++){StaticModInt<Mod>x=0;for(int i=0;i<lc;i++)x+=c[i]*s[k-i];for(int i=lb-1;i>=0;i--)b[i+1]=b[i];b[0]=0;lb++;if(x==0)continue;var v=x/y;if(lb>lc){for(int i=0;i<lb;i++)b[i]=c[i]-v*b[i];(c,b)=(b,c);(lb,lc)=(lc,lb);y=x;}else for(int i=0;i<lb;i++)c[i]-=v*b[i];}return c[0..lc].ToArray();}}}
namespace Lib.MathLib{public static class BostanMori<TMod>where TMod:struct,IStaticMod{static TMod op=default;public static StaticModInt<TMod>CalcNaive(ReadOnlySpan<StaticModInt<TMod>>p,ReadOnlySpan<StaticModInt<TMod>>q,long n){var a=p.ToArray();var b=q.ToArray();if(a.Length<b.Length)Array.Resize(ref a,b.Length);while(n>0){var a1=new StaticModInt<TMod>[a.Length+b.Length-1];var b1=new StaticModInt<TMod>[b.Length*2-1];for(int i=0;i<a.Length;i++)for(int j=0;j<b.Length;j++)if(j%2==0)a1[i+j]+=a[i]*b[j];else a1[i+j]-=a[i]*b[j];for(int i=0;i<b.Length;i++)for(int j=0;j<b.Length;j++)if(j%2==0)b1[i+j]+=b[i]*b[j];else b1[i+j]-=b[i]*b[j];int r=(int)(n%2);for(int i=0;i<a.Length&&i*2+r<a1.Length;i++)a[i]=a1[i*2+r];for(int i=0;i<b.Length;i++)b[i]=b1[i*2];n/=2;}return a[0]/b[0];}public static StaticModInt<TMod>CalcConvolution(ReadOnlySpan<StaticModInt<TMod>>p,ReadOnlySpan<StaticModInt<TMod>>q,long n){var a=p.ToArray();var b=q.ToArray();if(a.Length<b.Length)Array.Resize(ref a,b.Length);while(n>0){var c=new StaticModInt<TMod>[b.Length];for(int i=0;i<b.Length;i++)c[i]=i%2==0?b[i]:-b[i];var a1=Convolution.Calc<TMod>(a,c);var b1=Convolution.Calc<TMod>(b,c);int r=(int)(n%2);for(int i=0;i<a.Length&&i*2+r<a1.Length;i++)a[i]=a1[i*2+r];for(int i=0;i<b.Length;i++)b[i]=b1[i*2];n/=2;}return a[0]/b[0];}public static StaticModInt<TMod>CalcConvolutionAnyMod(ReadOnlySpan<StaticModInt<TMod>>p,ReadOnlySpan<StaticModInt<TMod>>q,long n){var a=new long[p.Length];for(int i=0;i<p.Length;i++)a[i]=p[i];var b=new long[q.Length];for(int i=0;i<q.Length;i++)b[i]=q[i];if(a.Length<b.Length)Array.Resize(ref a,b.Length);while(n>0){var c=new long[b.Length];for(int i=0;i<b.Length;i++)c[i]=i%2==0?b[i]:InternalMath.SafeMod(-b[i]+op.Mod,op.Mod);var a1=Convolution.Long(a,c);var b1=Convolution.Long(b,c);int r=(int)(n%2);for(int i=0;i<a.Length&&i*2+r<a1.Length;i++)a[i]=InternalMath.SafeMod(a1[i*2+r],op.Mod);for(int i=0;i<b.Length;i++)b[i]=InternalMath.SafeMod(b1[i*2],op.Mod);n/=2;}return a[0]/b[0];}public static class LinearReccurence{public static StaticModInt<TMod>Convolution(ReadOnlySpan<StaticModInt<TMod>>a,ReadOnlySpan<StaticModInt<TMod>>x,long n){var q=CalcQ(a,x);var p=new StaticModInt<TMod>[a.Length];for(int i=0;i<a.Length;i++)for(int j=0;i+j<a.Length;j++)p[i+j]+=q[i]*x[j];return CalcConvolution(p,q,n);}public static StaticModInt<TMod>ConvolutionAnyMod(ReadOnlySpan<StaticModInt<TMod>>a,ReadOnlySpan<StaticModInt<TMod>>x,long n){var q=CalcQ(a,x);var p=new StaticModInt<TMod>[a.Length];for(int i=0;i<a.Length;i++)for(int j=0;i+j<a.Length;j++)p[i+j]+=q[i]*x[j];return CalcConvolutionAnyMod(p,q,n);}public static StaticModInt<TMod>Naive(ReadOnlySpan<StaticModInt<TMod>>a,ReadOnlySpan<StaticModInt<TMod>>x,long n){var q=CalcQ(a,x);var p=new StaticModInt<TMod>[a.Length];for(int i=0;i<a.Length;i++)for(int j=0;i+j<a.Length;j++)p[i+j]+=q[i]*x[j];return CalcNaive(p,q,n);}private static StaticModInt<TMod>[]CalcQ(ReadOnlySpan<StaticModInt<TMod>>a,ReadOnlySpan<StaticModInt<TMod>>x){var q=new StaticModInt<TMod>[a.Length+1];q[0]=1;for(int i=0;i<a.Length;i++)q[i+1]=-a[i];return q;}}}}
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();}}
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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