Problem:
Dudeney Number

　

A Dudeney number is a positive integer for which the sum of its decimal digits is equal to the cube root of the number. For example, $512$ is a Dudeney number because it is the cube of $8$, which is the sum of its decimal digits ($5 + 1 + 2$).

In this problem, we think of a type similar to Dudeney numbers and try to enumerate them.

Given a non-negative integer $a$, an integer $n$ greater than or equal to 2 and an upper limit $m$, make a program to enumerate all $x$’s such that the sum of its decimal digits $y$ satisfies the relation $x = (y + a)^n$, and $x \leq m$.

Input

The input is given in the following format.

$a$ $n$ $m$

The input line provides three integers: $a$ ($0 \leq a \leq 50$), $n$ ($2 \leq n \leq 10$) and the upper limit $m$ ($1000 \leq m \leq 10^8$).

Output

Output the number of integers that meet the above criteria.

Sample Input 1

16 2 1000

Sample Output 1

2

Two: $400 = (4 + 0 + 0 + 16)^2$ and $841 = (8 + 4 + 1 + 16)^2$

Sample Input 2

0 3 5000

Sample Output 2

3

Three: $1=1^3$, $512 = (5 + 1 + 2)^3$ and $4913 = (4 + 9 + 1 + 3)^3$.

Sample Input 3

2 3 100000

Sample Output 3

0

There is no such number $x$ in the range below $100,000$ such that its sum of decimal digits $y$ satisfies the relation $(y+2)^3 = x$.

Solution in C# (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

class MyClass
{
    public static void Main(string[] args)
    {
        var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var a = input[0];
        var n = input[1];
        var m = input[2];
        var count = 0;
        for (int i = Math.Max(a, 1); i < m; i++)
        {
            var x = Math.Pow(i, n);
            if (x > m)
            {
                break;
            }
            var y = x.ToString().ToArray().Select(s => int.Parse(s.ToString())).Sum();
            if (i == y + a)
            {
                count++;
            }

        }
        Console.WriteLine(count);
    }
}