// knapsack problem
public class Solution
{
    public int NumberOfWays(int n, int x)
    {
        const int MOD = 1_000_000_007;
        // list all the powers which smaller than n
        var powers = new List<int>();
        var num = 1;

        while (true)
        {
            int pow = (int)Math.Pow(num, x);
            if (pow > n)
                break;
            powers.Add(pow);
            num++;
        }

        // dynamic programming
        var dp = new int[n + 1];
        dp[0] = 1;

        foreach (var power in powers)
        {
            for (var i = n; i >= power; i--)
            {
                dp[i] = (dp[i] + dp[i - power]) % MOD;
            }
        }

        return dp[n];

    }

}

class Program
{
    static void Main()
    {
        var solution = new Solution();

        Console.WriteLine(solution.NumberOfWays(4, 1));
        Console.WriteLine(solution.NumberOfWays(100, 3));

    }
}