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.IO;
using System.Collections;
using System.Collections.Generic;
using System.Text;

namespace Competitive_Programming
{
	class MainClass
	{
		static long f(long b, long n)
		{
			if (n < b) return n;
			return f(b, n / b) + (n % b);
		}

		public static void Main(string[] args)
		{
			long n = long.Parse(Console.ReadLine());
			long s = long.Parse(Console.ReadLine());
			long ans = (long)1e18;
			for (long i = 2; i * i <= n; i++)
			{
				if (f(i, n) == s)
				{
					ans = Math.Min(ans, i);
				}
			}
			for (long i = 2; i * i <= n; i++)
			{
				if ((n - s) % i != 0) continue;
				long b = ((n - s) / i) + 1;
				if (f(b, n) == s)
				{
					ans = Math.Min(ans, b);
				}
			}
			Console.WriteLine(ans!=(long)1e18?ans:-1);
		}
	}
}