using System;
using System.Buffers;
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.Runtime.Intrinsics.X86;
using System.Text;
using YukicoderContest316.Problems;
using ModInt = YukicoderContest316.Numerics.StaticModInt<YukicoderContest316.Numerics.Mod998244353>;

namespace YukicoderContest316.Problems
{
    public class ProblemB : ProblemBase
    {
        public ProblemB() : base(false) { }

        [MethodImpl(MethodImplOptions.AggressiveOptimization)]
        protected override void SolveEach(IOManager io)
        {
            var n = io.ReadInt();
            var m = io.ReadInt();
            var a = io.ReadIntArray(n);
            var comb = new Numerics.ModCombination<Numerics.Mod998244353>();

            var distances = new int[m + 1];
            const int INF = int.MaxValue / 2;
            distances.Fill(INF);
            distances[0] = 0;

            for (int i = 0; i < distances.Length; i++)
            {
                for (int j = 0; j < a.Length; j++)
                {
                    var next = i + a[j];

                    if (next < distances.Length)
                    {
                        distances[next].ChangeMin(distances[i] + 1);
                    }
                }
            }

            var result = ModInt.Zero;

            for (int i = 0; i < distances.Length; i++)
            {
                var remain = i - distances[i];
                if (remain >= 0)
                {
                    result += comb.Combination(m - distances[i], remain);
                }
            }

            io.WriteLine(result);
        }
    }
}

namespace YukicoderContest316
{
    class Program
    {
        static void Main(string[] args)
        {
            IProblem question = new ProblemB();
            using var io = new IOManager(Console.OpenStandardInput(), Console.OpenStandardOutput());
            question.Solve(io);
        }
    }
}

#region Base Class

namespace YukicoderContest316.Problems
{
    public interface IProblem
    {
        string Solve(string input);
        void Solve(IOManager io);
    }

    public abstract class ProblemBase : IProblem
    {
        protected bool HasMultiTestCases { get; }

        protected ProblemBase(bool hasMultiTestCases) => HasMultiTestCases = hasMultiTestCases;

        public string Solve(string input)
        {
            var inputStream = new MemoryStream(Encoding.UTF8.GetBytes(input));
            var outputStream = new MemoryStream();
            using var manager = new IOManager(inputStream, outputStream);

            Solve(manager);
            manager.Flush();

            outputStream.Seek(0, SeekOrigin.Begin);
            var reader = new StreamReader(outputStream);
            return reader.ReadToEnd();
        }

        public void Solve(IOManager io)
        {
            var tests = HasMultiTestCases ? io.ReadInt() : 1;

            for (var t = 0; t < tests; t++)
            {
                SolveEach(io);
            }
        }

        protected abstract void SolveEach(IOManager io);
    }
}

#endregion

#region Utils

namespace YukicoderContest316
{
    public class IOManager : IDisposable
    {
        private readonly BinaryReader _reader;
        private readonly StreamWriter _writer;
        private bool _disposedValue;
        private byte[] _buffer = new byte[1024];
        private int _length;
        private int _cursor;
        private bool _eof;

        const char ValidFirstChar = '!';
        const char ValidLastChar = '~';

        public IOManager(Stream input, Stream output)
        {
            _reader = new BinaryReader(input);
            _writer = new StreamWriter(output) { AutoFlush = false };
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private char ReadAscii()
        {
            if (_cursor == _length)
            {
                _cursor = 0;
                _length = _reader.Read(_buffer);

                if (_length == 0)
                {
                    if (!_eof)
                    {
                        _eof = true;
                        return char.MinValue;
                    }
                    else
                    {
                        ThrowEndOfStreamException();
                    }
                }
            }

            return (char)_buffer[_cursor++];
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public char ReadChar()
        {
            char c;
            while (!IsValidChar(c = ReadAscii())) { }
            return c;
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public string ReadString()
        {
            var builder = new StringBuilder();
            char c;
            while (!IsValidChar(c = ReadAscii())) { }

            do
            {
                builder.Append(c);
            } while (IsValidChar(c = ReadAscii()));

            return builder.ToString();
        }

        public int ReadInt() => (int)ReadLong();

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public long ReadLong()
        {
            long result = 0;
            bool isPositive = true;
            char c;

            while (!IsNumericChar(c = ReadAscii())) { }

            if (c == '-')
            {
                isPositive = false;
                c = ReadAscii();
            }

            do
            {
                result *= 10;
                result += c - '0';
            } while (IsNumericChar(c = ReadAscii()));

            return isPositive ? result : -result;
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private Span<char> ReadChunk(Span<char> span)
        {
            var i = 0;
            char c;
            while (!IsValidChar(c = ReadAscii())) { }

            do
            {
                span[i++] = c;
            } while (IsValidChar(c = ReadAscii()));

            return span.Slice(0, i);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public double ReadDouble() => double.Parse(ReadChunk(stackalloc char[32]));

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public decimal ReadDecimal() => decimal.Parse(ReadChunk(stackalloc char[32]));

        public int[] ReadIntArray(int n)
        {
            var a = new int[n];
            for (int i = 0; i < a.Length; i++)
            {
                a[i] = ReadInt();
            }
            return a;
        }

        public long[] ReadLongArray(int n)
        {
            var a = new long[n];
            for (int i = 0; i < a.Length; i++)
            {
                a[i] = ReadLong();
            }
            return a;
        }

        public double[] ReadDoubleArray(int n)
        {
            var a = new double[n];
            for (int i = 0; i < a.Length; i++)
            {
                a[i] = ReadDouble();
            }
            return a;
        }

        public decimal[] ReadDecimalArray(int n)
        {
            var a = new decimal[n];
            for (int i = 0; i < a.Length; i++)
            {
                a[i] = ReadDecimal();
            }
            return a;
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Write<T>(T value) => _writer.Write(value.ToString());

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void WriteLine<T>(T value) => _writer.WriteLine(value.ToString());

        public void WriteLine<T>(IEnumerable<T> values, char separator)
        {
            var e = values.GetEnumerator();
            if (e.MoveNext())
            {
                _writer.Write(e.Current.ToString());

                while (e.MoveNext())
                {
                    _writer.Write(separator);
                    _writer.Write(e.Current.ToString());
                }
            }

            _writer.WriteLine();
        }

        public void WriteLine<T>(T[] values, char separator) => WriteLine((ReadOnlySpan<T>)values, separator);
        public void WriteLine<T>(Span<T> values, char separator) => WriteLine((ReadOnlySpan<T>)values, separator);

        public void WriteLine<T>(ReadOnlySpan<T> values, char separator)
        {
            for (int i = 0; i < values.Length - 1; i++)
            {
                _writer.Write(values[i]);
                _writer.Write(separator);
            }

            if (values.Length > 0)
            {
                _writer.Write(values[^1]);
            }

            _writer.WriteLine();
        }

        public void Flush() => _writer.Flush();

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private static bool IsValidChar(char c) => ValidFirstChar <= c && c <= ValidLastChar;

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private static bool IsNumericChar(char c) => ('0' <= c && c <= '9') || c == '-';

        private void ThrowEndOfStreamException() => throw new EndOfStreamException();

        protected virtual void Dispose(bool disposing)
        {
            if (!_disposedValue)
            {
                if (disposing)
                {
                    _reader.Dispose();
                    _writer.Flush();
                    _writer.Dispose();
                }

                _disposedValue = true;
            }
        }

        public void Dispose()
        {
            Dispose(disposing: true);
            GC.SuppressFinalize(this);
        }
    }

    public static class UtilExtensions
    {
        public static bool ChangeMax<T>(ref this T value, T other) where T : struct, IComparable<T>
        {
            if (value.CompareTo(other) < 0)
            {
                value = other;
                return true;
            }
            return false;
        }

        public static bool ChangeMin<T>(ref this T value, T other) where T : struct, IComparable<T>
        {
            if (value.CompareTo(other) > 0)
            {
                value = other;
                return true;
            }
            return false;
        }

        public static void SwapIfLargerThan<T>(ref this T a, ref T b) where T : struct, IComparable<T>
        {
            if (a.CompareTo(b) > 0)
            {
                (a, b) = (b, a);
            }
        }

        public static void SwapIfSmallerThan<T>(ref this T a, ref T b) where T : struct, IComparable<T>
        {
            if (a.CompareTo(b) < 0)
            {
                (a, b) = (b, a);
            }
        }

        public static void Sort<T>(this T[] array) where T : IComparable<T> => Array.Sort(array);
        public static void Sort<T>(this T[] array, Comparison<T> comparison) => Array.Sort(array, comparison);
    }

    public static class CollectionExtensions
    {
        private class ArrayWrapper<T>
        {
#pragma warning disable CS0649
            public T[] Array;
#pragma warning restore CS0649
        }

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

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static Span<T> GetRowSpan<T>(this T[,] array, int i)
        {
            var width = array.GetLength(1);
            return MemoryMarshal.CreateSpan(ref array[i, 0], width);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static Span<T> GetRowSpan<T>(this T[,,] array, int i, int j)
        {
            var width = array.GetLength(2);
            return MemoryMarshal.CreateSpan(ref array[i, j, 0], width);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static Span<T> GetRowSpan<T>(this T[,,,] array, int i, int j, int k)
        {
            var width = array.GetLength(3);
            return MemoryMarshal.CreateSpan(ref array[i, j, k, 0], width);
        }

        public static void Fill<T>(this T[] array, T value) => array.AsSpan().Fill(value);
        public static void Fill<T>(this T[,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0], array.Length).Fill(value);
        public static void Fill<T>(this T[,,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0, 0], array.Length).Fill(value);
        public static void Fill<T>(this T[,,,] array, T value) => MemoryMarshal.CreateSpan(ref array[0, 0, 0, 0], array.Length).Fill(value);
    }

    public static class SearchExtensions
    {
        struct LowerBoundComparer<T> : IComparer<T> where T : IComparable<T>
        {
            public int Compare(T x, T y) => 0 <= x.CompareTo(y) ? 1 : -1;
        }

        struct UpperBoundComparer<T> : IComparer<T> where T : IComparable<T>
        {
            public int Compare(T x, T y) => 0 < x.CompareTo(y) ? 1 : -1;
        }

        // https://trsing.hatenablog.com/entry/2019/08/27/211038
        public static int GetGreaterEqualIndex<T>(this ReadOnlySpan<T> span, T inclusiveMin) where T : IComparable<T> => ~span.BinarySearch(inclusiveMin, new UpperBoundComparer<T>());
        public static int GetGreaterThanIndex<T>(this ReadOnlySpan<T> span, T exclusiveMin) where T : IComparable<T> => ~span.BinarySearch(exclusiveMin, new LowerBoundComparer<T>());
        public static int GetLessEqualIndex<T>(this ReadOnlySpan<T> span, T inclusiveMax) where T : IComparable<T> => ~span.BinarySearch(inclusiveMax, new LowerBoundComparer<T>()) - 1;
        public static int GetLessThanIndex<T>(this ReadOnlySpan<T> span, T exclusiveMax) where T : IComparable<T> => ~span.BinarySearch(exclusiveMax, new UpperBoundComparer<T>()) - 1;
        public static int GetGreaterEqualIndex<T>(this Span<T> span, T inclusiveMin) where T : IComparable<T> => ((ReadOnlySpan<T>)span).GetGreaterEqualIndex(inclusiveMin);
        public static int GetGreaterThanIndex<T>(this Span<T> span, T exclusiveMin) where T : IComparable<T> => ((ReadOnlySpan<T>)span).GetGreaterThanIndex(exclusiveMin);
        public static int GetLessEqualIndex<T>(this Span<T> span, T inclusiveMax) where T : IComparable<T> => ((ReadOnlySpan<T>)span).GetLessEqualIndex(inclusiveMax);
        public static int GetLessThanIndex<T>(this Span<T> span, T exclusiveMax) where T : IComparable<T> => ((ReadOnlySpan<T>)span).GetLessThanIndex(exclusiveMax);

        public static int BoundaryBinarySearch(Predicate<int> predicate, int ok, int ng)
        {
            while (Math.Abs(ok - ng) > 1)
            {
                var mid = (ok + ng) / 2;
                if (predicate(mid))
                {
                    ok = mid;
                }
                else
                {
                    ng = mid;
                }
            }
            return ok;
        }

        public static long BoundaryBinarySearch(Predicate<long> predicate, long ok, long ng)
        {
            while (Math.Abs(ok - ng) > 1)
            {
                var mid = (ok + ng) / 2;
                if (predicate(mid))
                {
                    ok = mid;
                }
                else
                {
                    ng = mid;
                }
            }
            return ok;
        }

        public static BigInteger BoundaryBinarySearch(Predicate<BigInteger> predicate, BigInteger ok, BigInteger ng)
        {
            while (BigInteger.Abs(ok - ng) > 1)
            {
                var mid = (ok + ng) / 2;
                if (predicate(mid))
                {
                    ok = mid;
                }
                else
                {
                    ng = mid;
                }
            }
            return ok;
        }

        public static double BoundaryBinarySearch(Predicate<double> predicate, double ok, double ng, double eps = 1e-9, int loopLimit = 1000)
        {
            var count = 0;

            while (Math.Abs(ok - ng) > eps && count++ < loopLimit)
            {
                var mid = (ok + ng) * 0.5;
                if (predicate(mid))
                {
                    ok = mid;
                }
                else
                {
                    ng = mid;
                }
            }

            return (ok + ng) * 0.5;
        }

        public static double Bisection(Func<double, double> f, double a, double b, double eps = 1e-9, int loopLimit = 100)
        {
            double mid = (a + b) / 2;
            var fa = f(a);

            if (fa * f(b) >= 0)
            {
                throw new ArgumentException("f(a)とf(b)は異符号である必要があります。");
            }

            for (int i = 0; i < loopLimit; i++)
            {
                var fmid = f(mid);
                var sign = fa * fmid;

                if (sign < 0)
                {
                    b = mid;
                }
                else if (sign > 0)
                {
                    a = mid;
                    fa = fmid;
                }
                else
                {
                    return mid;
                }

                mid = (a + b) / 2;

                if (Math.Abs(b - a) < eps)
                {
                    break;
                }
            }
            return mid;
        }
    }
}

#endregion

namespace YukicoderContest316.Numerics
{
    #region ModInt

    /// <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&lt;AtCoder.Mod1000000007&gt;;
    ///
    /// void SomeMethod()
    /// {
    ///     var m = new ModInt(1);
    ///     m -= 2;
    ///     Console.WriteLine(m);   // 1000000006
    /// }
    /// </code>
    /// </example>
    public readonly struct StaticModInt<T> : IEquatable<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;

        public static StaticModInt<T> Zero => new StaticModInt<T>();
        public static StaticModInt<T> One => new StaticModInt<T>(1u);

        /// <summary>
        /// <paramref name="v"/> に対して mod を取らずに StaticModInt&lt;<typeparamref name="T"/>&gt; 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"/>|&lt;mod</para>
        /// </remarks>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static StaticModInt<T> Raw(int v)
        {
            var u = unchecked((uint)v);
            Debug.Assert(u < Mod);
            return new StaticModInt<T>(u);
        }

        /// <summary>
        /// StaticModInt&lt;<typeparamref name="T"/>&gt; 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;

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private static uint Round(long v)
        {
            var x = v % default(T).Mod;
            if (x < 0)
            {
                x += default(T).Mod;
            }
            return (uint)x;
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        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);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        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);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        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);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        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);
            }
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        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.Inverse();

        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 = Raw(1);

            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>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public StaticModInt<T> Inverse()
        {
            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> && Equals((StaticModInt<T>)obj);
        public bool Equals(StaticModInt<T> other) => Value == other.Value;
        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&lt;<typeparamref name="T"/>&gt;.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&lt;AtCoder.ModID0&gt;;
    ///
    /// void SomeMethod()
    /// {
    ///     ModInt.Mod = 1000000009;
    ///     var m = new ModInt(1);
    ///     m -= 2;
    ///     Console.WriteLine(m);   // 1000000008
    /// }
    /// </code>
    /// </example>
    public readonly struct DynamicModInt<T> : IEquatable<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&lt;<typeparamref name="T"/>&gt; 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"/>|&lt;mod</para>
        /// </remarks>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        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&lt;<typeparamref name="T"/>&gt; 型のインスタンスを生成します。
        /// </summary>
        /// <remarks>
        /// <para>- 使用前に DynamicModInt&lt;<typeparamref name="T"/>&gt;.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;

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        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;
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static DynamicModInt<T> operator ++(DynamicModInt<T> value)
        {
            var v = value._v + 1;
            if (v == bt.Mod)
            {
                v = 0;
            }
            return new DynamicModInt<T>(v);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static DynamicModInt<T> operator --(DynamicModInt<T> value)
        {
            var v = value._v;
            if (v == 0)
            {
                v = bt.Mod;
            }
            return new DynamicModInt<T>(v - 1);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        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);
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        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);
            }
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        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.Inverse();

        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 = Raw(1);

            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>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public DynamicModInt<T> Inverse()
        {
            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> && Equals((DynamicModInt<T>)obj);
        public bool Equals(DynamicModInt<T> other) => Value == other.Value;
        public override int GetHashCode() => _v.GetHashCode();
    }

    /// <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;
            if (!Bmi2.X64.IsSupported) return (uint)(z % Mod);
            var x = Bmi2.X64.MultiplyNoFlags(z, IM);
            var v = unchecked((uint)(z - x * Mod));
            if (Mod <= v) v += Mod;
            return v;
        }
    }

    public static class InternalMath
    {
        /// <summary>
        /// g=gcd(a,b),xa=g(mod b) となるような 0≤x&lt;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;
            }
        }

        public static long SafeMod(long x, long m)
        {
            x %= m;
            if (x < 0) x += m;
            return x;
        }
    }

    public class ModCombination<T> where T : struct, IStaticMod
    {
        readonly StaticModInt<T>[] _factorials;
        readonly StaticModInt<T>[] _invFactorials;

        public ModCombination(int max = 1000000)
        {
            if (max >= default(T).Mod)
            {
                ThrowArgumentOutOfRangeException();
            }

            _factorials = new StaticModInt<T>[max + 1];
            _invFactorials = new StaticModInt<T>[max + 1];

            _factorials[0] = _factorials[1] = StaticModInt<T>.Raw(1);
            _invFactorials[0] = _invFactorials[1] = StaticModInt<T>.Raw(1);

            for (int i = 2; i < _factorials.Length; i++)
            {
                _factorials[i] = _factorials[i - 1] * StaticModInt<T>.Raw(i);
            }

            _invFactorials[^1] = _factorials[^1].Inverse();

            for (int i = _invFactorials.Length - 2; i >= 0; i--)
            {
                _invFactorials[i] = _invFactorials[i + 1] * StaticModInt<T>.Raw(i + 1);
            }
        }

        public StaticModInt<T> Factorial(int n) => _factorials[n];

        public StaticModInt<T> Permutation(int n, int k) => _factorials[n] * _invFactorials[n - k];

        public StaticModInt<T> Combination(int n, int k) => _factorials[n] * _invFactorials[k] * _invFactorials[n - k];

        public StaticModInt<T> CombinationWithRepetition(int n, int k) => Combination(n + k - 1, k);

        public void ThrowArgumentOutOfRangeException() => throw new ArgumentOutOfRangeException();
    }

    #endregion

}