Happy Tickets

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;

namespace Tickets
{
    class Solver
    {
        public static BigInteger Zero = BigInteger.Zero;
        public static BigInteger One = BigInteger.One;
        public static BigInteger NegativOne = BigInteger.MinusOne;

        static BigInteger QuantityHappyTickets(int len, int sum, BigInteger[,] memory)
        {
            if (memory[len, sum] >= Zero)
            {
                return memory[len, sum];
            }

            if (len == 0)
            {
                return sum == 0 ? One : Zero;
            }

            memory[len, sum] = Zero;

            for (int i = 0; i < 10; i++)
            {
                if (sum - i < 0) continue;
                memory[len, sum] = BigInteger.Add(memory[len, sum], QuantityHappyTickets(len - 1, sum - i, memory));
            }

            return memory[len, sum];
        }

        public static BigInteger Solve(int totalLen, int totalSum)
        {
            var memory = new BigInteger[51, 1001];

            if (totalSum%2 != 0)
            {
                return 0;
            }

            totalSum /= 2;

            for (int i = 0; i < totalLen + 1; i++)
            {
                for (int j = 0; j < totalSum + 1; j++)
                {
                    memory[i, j] = NegativOne;
                }
            }

            return QuantityHappyTickets(totalLen, totalSum, memory)*QuantityHappyTickets(totalLen, totalSum, memory);
        }
    }
}