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: Accepted)

using System;

class quiz
{
    public long solve(long n, long s)
    {
        long digit = 0, sum = 0;
        long num = n, ans = -1;

        if (s > n / 2 + n % 2 && s != n)
            return -1;
        
        if (s == n)
            return n + 1;

        for (int i = 2; i <= Math.Pow(n, 0.5); i++)
        {
            digit = 0;
            num = n;
            sum = 0;

            for (long j = 0; Math.Pow(i, j) <= n; j++)
            {
                digit = j;
            }

            for (long j = digit; j >= 0; j--)
            {
                sum += (long)(num / ((long)Math.Pow(i, j)));
                num -= (long)(num / ((long)Math.Pow(i, j))) * (long)Math.Pow(i, j);
            }

            if (sum == s)
                return i;
        }

        for (int i = 1; i < Math.Pow(n, 0.5); i++)
        {
            if (((s - n % i) % i == 0) && (s - n % i) / i > 0 && (s - n % i) / i <= n / i - n / (i + 1) + 1)
            {
                ans = (long)n / i - (long)(s - n % i) / i + 1;
            }
        }

        return ans;
    }

    public int[] ParseIntBySpace(string str)
    {
        int[] array = new int[str.Length];
        int lastloc = 0, spaceloc = -1;

        for (int i = 0; i < str.Length; i++)
        {
            if (str[i] == ' ')
            {
                array[lastloc++] = int.Parse(str.Substring(spaceloc + 1, i - spaceloc - 1));
                spaceloc = i;
            }
            else if (i == str.Length - 1)
            {
                array[lastloc++] = int.Parse(str.Substring(spaceloc + 1, i - spaceloc));
            }
        }

        Array.Resize(ref array, lastloc);

        return array;
    }
}

class Example
{
    static void Main()
    {
        quiz ex = new quiz();

        //while (true)
        //{
            Console.WriteLine(ex.solve(long.Parse(Console.ReadLine()), long.Parse(Console.ReadLine())));
        //}
    }
}