using System; using System.Linq; using System.Linq.Expressions; using System.Collections.Generic; using Debug = System.Diagnostics.Debug; using StringBuilder = System.Text.StringBuilder; using System.Numerics; using Point = System.Numerics.Complex; using Number = ModInteger; namespace Program { public class Solver { public void Solve() { var dp = new ModInteger[5001]; var A = new int[] { 1, 5, 10, 50, 100, 500 }; dp[0] = 1; for (int i = 0; i < 6; i++) { for (int j = A[i]; j < dp.Length; j++) dp[j] += dp[j - A[i]]; } Debug.WriteLine(dp.AsJoinedString()); var T = sc.Integer(); for (int _ = 0; _ < T; _++) { var x = sc.Long(); var a = x / 500; var b = (int)(x % 500); if (x < dp.Length) IO.Printer.Out.WriteLine(dp[x]); else { var xs = new long[6]; var fxs = new ModInteger[6]; for (int i = 0; i < 6; i++) { xs[i] = i; fxs[i] = dp[i * 500 + b]; } var lg = new LagrangeInterpolator(xs, fxs); IO.Printer.Out.WriteLine(lg.F(a)); } } } public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput()); static T[] Enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; } static public void Swap(ref T a, ref T b) { var tmp = a; a = b; b = tmp; } } } #region main static class Ex { static public string AsString(this IEnumerable ie) { return new string(System.Linq.Enumerable.ToArray(ie)); } static public string AsJoinedString(this IEnumerable ie, string st = " ") { return string.Join(st, ie); } static public void Main() { var solver = new Program.Solver(); solver.Solve(); Program.IO.Printer.Out.Flush(); } } #endregion #region Ex namespace Program.IO { using System.IO; using System.Text; using System.Globalization; public class Printer : StreamWriter { static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; } public static Printer Out { get; set; } public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { } public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { } public void Write(string format, T[] source) { base.Write(format, source.OfType().ToArray()); } public void WriteLine(string format, T[] source) { base.WriteLine(format, source.OfType().ToArray()); } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } public readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) return 0; if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public string ScanLine() { var sb = new StringBuilder(); for (var b = Char(); b != '\n'; b = (char)read()) if (b == 0) break; else if (b != '\r') sb.Append(b); return sb.ToString(); } public long Long() { if (isEof) return long.MinValue; long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b)); if (b == 0) return long.MinValue; 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'; } } public int Integer() { return (isEof) ? int.MinValue : (int)Long(); } public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; } private T[] enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(); return a; } public char[] Char(int n) { return enumerate(n, Char); } public string[] Scan(int n) { return enumerate(n, Scan); } public double[] Double(int n) { return enumerate(n, Double); } public int[] Integer(int n) { return enumerate(n, Integer); } public long[] Long(int n) { return enumerate(n, Long); } } } #endregion #region Lagrange interpolation public class LagrangeInterpolator { long[] X; Number[] Fx; public LagrangeInterpolator(long[] X, Number[] Fx) { this.X = X.ToArray(); this.Fx = Fx.ToArray(); } public Number F(long x) { Number ret = 0; for (int i = 0; i < X.Length; i++) { Number U = 1; Number D = 1; for (int j = 0; j < X.Length; j++) if (j != i) { U *= x - X[j]; D *= X[i] - X[j]; } ret += (U * ModInteger.Inverse(D)) * Fx[i]; } return ret; } } #endregion #region ModNumber public partial struct ModInteger { public const long Mod = (long)1e9 + 9; public long num; public ModInteger(long n) : this() { num = n % Mod; if (num < 0) num += Mod; } public override string ToString() { return num.ToString(); } public static ModInteger operator +(ModInteger l, ModInteger r) { var n = l.num + r.num; if (n >= Mod) n -= Mod; return new ModInteger() { num = n }; } public static ModInteger operator -(ModInteger l, ModInteger r) { var n = l.num + Mod - r.num; if (n >= Mod) n -= Mod; return new ModInteger() { num = n }; } public static ModInteger operator *(ModInteger l, ModInteger r) { return new ModInteger(l.num * r.num); } public static ModInteger operator ^(ModInteger l, long r) { return ModInteger.Pow(l, r); } public static implicit operator ModInteger(long n) { return new ModInteger(n); } public static ModInteger Pow(ModInteger v, long k) { ModInteger ret = 1; var n = k; for (; n > 0; n >>= 1, v *= v) { if ((n & 1) == 1) ret = ret * v; } return ret; } } #endregion #region Inverse public partial struct ModInteger { static public ModInteger Inverse(ModInteger v) { long p, q; ExGCD(v.num, Mod, out p, out q); return new ModInteger(p % Mod + Mod); } static public long ExGCD(long a, long b, out long x, out long y) { var u = new long[] { a, 1, 0 }; var v = new long[] { b, 0, 1 }; while (v[0] != 0) { var t = u[0] / v[0]; for (int i = 0; i < 3; i++) { var tmp = u[i] - t * v[i]; u[i] = v[i]; v[i] = tmp; } } x = u[1]; y = u[2]; if (u[0] > 0) return u[0]; for (int i = 0; i < 3; i++) u[i] = -u[i]; return u[0]; } } #endregion