Problem:
Score : 500 points

Problem Statement

For integers b (b \geq 2) and n (n \geq 1), let the function f(b,n) be defined as follows:

f(b,n) = n, when n < b

f(b,n) = f(b,\,{\rm floor}(n / b)) + (n \ {\rm mod} \ b), when n \geq b

Here, {\rm floor}(n / b) denotes the largest integer not exceeding n / b,
and n \ {\rm mod} \ b denotes the remainder of n divided by b.

Less formally, f(b,n) is equal to the sum of the digits of n written in base b.
For example, the following hold:

f(10,\,87654)=8+7+6+5+4=30

f(100,\,87654)=8+76+54=138

You are given integers n and s.
Determine if there exists an integer b (b \geq 2) such that f(b,n)=s.
If the answer is positive, also find the smallest such b.

Constraints

1 \leq n \leq 10^{11}

1 \leq s \leq 10^{11}

n,\,s are integers.

Input

The input is given from Standard Input in the following format:

n
s

Output

If there exists an integer b (b \geq 2) such that f(b,n)=s, print the smallest such b.
If such b does not exist, print -1 instead.

Sample Input 1

87654
30

Sample Output 1

10

Sample Input 2

87654
138

Sample Output 2

100

Sample Input 3

87654
45678

Sample Output 3

-1

Sample Input 4

31415926535
1

Sample Output 4

31415926535

Sample Input 5

1
31415926535

Sample Output 5

-1

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

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

namespace D
{
    class Program
    {
        static long f(long b, long n)
        {
            if (n < b) { return n; }
            else { return f(b, (long)Math.Floor((double)n / b)) + n % b; }
        }
        static void Main(string[] args)
        {
            var N = long.Parse(Console.ReadLine());
            var S = long.Parse(Console.ReadLine());
            var ans = -1L;
            if (S == N) { ans = N + 1L; }
            else
            {
                var flag = false;
                var b = 2L;
                while (b <= Math.Sqrt(N))
                {
                    if (f(b, N) == S)
                    {
                        flag = true;
                        ans = b;
                        break;
                    }
                    b++;
                }
                if (!flag)
                {
                    var p = 1L;
                    while(p <= Math.Sqrt(N))
                    {
                        b = (N - S) / p + 1L;
                        if (f(b, N) == S) { ans = b; flag = true; break; }
                        p++; 
                    }
                }
            }
            Console.WriteLine(ans);
        }
    }
}