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.Text;
using System.Linq;


class Program
{
    public void Proc()
    {
        Reader.IsDebug = false;
        long n = long.Parse(Reader.ReadLine());
        long s = long.Parse(Reader.ReadLine());

        long ans = -1;
        if (s == 1)
        {
            ans = n;
        }
        else
        {
            for (long i = 2; i <= n; i++)
            {
                long ret = getF(i, n);
                if (s == ret)
                {
                    ans = i;
                    break;
                }
            }
        }
        Console.WriteLine(ans);
 
    }

    private Dictionary<long, Dictionary<long, long>> dic = new Dictionary<long, Dictionary<long, long>>();

    private long getF(long b, long n)
    {
        if (!dic.ContainsKey(b))
        {
            dic.Add(b, new Dictionary<long,long>());

        }
        if (dic[b].ContainsKey(n))
        {
            return dic[b][n];
        }

        long ans = 0;
        if (n < b)
        {
            ans = n;
        }
        else
        {
            ans =getF(b, n / b) + (n % b);
        }
        dic[b].Add(n, ans);
        return ans;
    }




    public class Reader
    {
        public static bool IsDebug = true;
        private static String PlainInput = @"


1
31415926535


";
        private static System.IO.StringReader Sr = null;
        public static string ReadLine()
        {
            if (IsDebug)
            {
                if (Sr == null)
                {
                    Sr = new System.IO.StringReader(PlainInput.Trim());
                }
                return Sr.ReadLine();
            }
            else
            {
                return Console.ReadLine();
            }
        }
    }
    static void Main()
    {
        Program prg = new Program();
        prg.Proc();
    }
}