Problem:
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Problem Statement

One day, my grandmas left $N$ cookies.
My elder sister and I were going to eat them immediately, but there was the instruction.
It said

Cookies will go bad; you should eat all of them within $D$ days.

Be careful about overeating; you should eat strictly less than $X$ cookies in a day.

My sister said "How many ways are there to eat all of the cookies? Let's try counting!"

Two ways are considered different if there exists a day such that the numbers of the cookies eaten on that day are different in the two ways.
For example, if $N$, $D$ and $X$ are $5$, $2$ and $5$ respectively, the number of the ways is $4$:

Eating $1$ cookie on the first day and $4$ cookies on the second day.

Eating $2$ cookies on the first day and $3$ cookies on the second day.

Eating $3$ cookies on the first day and $2$ cookies on the second day.

Eating $4$ cookies on the first day and $1$ cookie on the second day.

I noticed the number of the ways would be very huge and my sister would die before counting it.
Therefore, I tried to count it by a computer program to save the life of my sister.

Input

The input consists of multiple datasets.
The number of datasets is no more than $100$.
For each dataset, three numbers $N$ ($1 \le N \le 2{,}000$), $D$ ($1 \le D \le 10^{12}$) and $X$ ($1 \le X \le 2{,}000$) are written in a line and separated by a space.
The end of input is denoted by a line that contains three zeros.

Output

Print the number of the ways modulo $1{,}000{,}000{,}007$ in a line for each dataset.

Sample Input

5 2 5
3 3 3
5 4 5
4 1 2
1 5 1
1250 50 50
0 0 0

Output for the Sample Input

4
7
52
0
0
563144298

Solution in C# (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Debug;
using SB = System.Text.StringBuilder;
using System.Numerics;
using static System.Math;
using P = System.Numerics.Complex;
namespace Program {
    public class Solver {
        Random rnd = new Random();
        long[][] dp = Enumerate(2050, x => new long[2050]);
        public void Solve() {
            init();
            for (; ; )
            {
                var n = ri;
                if (n == 0) return;
                var d = rl;
                var x = ri;
                if (x == 1) { Console.WriteLine(0); continue; }
                for (int i = 0; i < dp.Length; i++)
                    for (int j = 0; j < dp[i].Length; j++)
                        dp[i][j] = 0;
                dp[0][0] = 1L;
                long ret = 0;
                for (int k = 1; k <= n; k++)
                {
                    for (int j = 0; j <= n; j++)
                        dp[k - 1][j + 1] = (dp[k - 1][j + 1] + dp[k - 1][j]) % MOD;
                    for (int j = 1; j <= n; j++)
                    {
                        dp[k][j] += dp[k - 1][j - 1];
                        if (j - x >= 0)
                            dp[k][j] += MOD - dp[k - 1][j - x];
                        dp[k][j] %= MOD;
                    }
                    ret = (ret + dp[k][n] * binomial(d, k)) % MOD;
                }
                Console.WriteLine(ret);
            }
        }
        long binomial(long n, long k) {
            var ret = 1L;
            var v = 1L;
            for (int i = 0; i < k; i++)
            {
                ret *= (n - i) % MOD;
                ret %= MOD;
                v *= i + 1;
                v %= MOD;
            }
            v = (long)BigInteger.ModPow(v, MOD - 2, MOD);
            return ret * v % MOD;
        }
        const long MOD = (long)1e9 + 7;
        long[,] comb;
        void init() {
            comb = new long[2050, 2050];
            comb[0, 0] = 1;
            for (int i = 0; i <= 2000; i++)
                for (int j = 0; j <= 2000; j++)
                {
                    comb[i, j] %= MOD;
                    comb[i + 1, j] += comb[i, j];
                    comb[i + 1, j + 1] += comb[i, j];
                }

        }
        const long INF = 1L << 60;
        int ri { get { return sc.Integer(); } }
        long rl { get { return sc.Long(); } }
        double rd { get { return sc.Double(); } }
        string rs { get { return sc.Scan(); } }
        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());

        static T[] Enumerate<T>(int n, Func<int, T> f) {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f(i);
            return a;
        }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex {
    static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
        return string.Join(st, ie);
    }
    static public void Main() {
        Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Program.Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO {
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer: StreamWriter {
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }

    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 != 0; b = (char)read()) if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
}

#endregion