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.IO;

using Pair = System.Collections.Generic.KeyValuePair<int, int>;

class Program
{
	public Program() { }

	static void Main(string[] args)
	{
		new Program().prog();
	}
	Scanner cin;
	const int MOD = 1000000007;
	const int INF = int.MaxValue;
	const double EPS = 1e-7;
	const double PI = 3.1415926536;

	void prog()
	{
		cin = new Scanner();
		int[,] dir8 = new int[8, 2] { { -1, -1 }, { -1, 0 }, { -1, 1 }, { 0, -1 }, { 0, 1 }, { 1, -1 }, { 1, 0 }, { 1, 1 } };
		int[,] dir4 = new int[4, 2] { { -1, 0 }, { 0, -1 }, { 0, 1 }, { 1, 0 } };

		long n = cin.nextLong();
		long s = cin.nextLong();
		if (s > n)
		{
			Console.WriteLine(-1);
			return;
		}
		List<int> list = new List<int>();
		for (int i = 2; i <= Math.Sqrt(n) + 0.5; i++)
		{
			long f = 0;
			long m = n;
			while (m > 0)
			{
				f += m % i;
				m /= i;
			}
			if (f == s)
			{
				Console.WriteLine(i);
				return;
			}
		}
		for (int i = 1; i <= Math.Sqrt(n - s) + 0.5; i++)
		{
			if ((n - s) % i == 0) list.Add(i);
		}
		for (int i = 1; i < list.Count; i++)
		{
			if (list[i] < Math.Sqrt(n)) continue;
			long b = list[i] + 1;
			long f = 0;
			long m = n;
			while (m > 0)
			{
				f += m % b;
				m /= b;
			}
			if (f == s)
			{
				Console.WriteLine(b);
				return;
			}
		}
		for (int i = list.Count - 1; i >= 0; i--)
		{
			long b = (n - s) / list[i] + 1;
			long f = 0;
			long m = n;
			while (m > 0)
			{
				f += m % b;
				m /= b;
			}
			if (f == s)
			{
				Console.WriteLine(b);
				return;
			}
		}
		if (n == s) Console.WriteLine(n);
		else Console.WriteLine(-1);
	}
}

class Scanner
{
	string[] s;
	int i;

	char[] cs = new char[] { ' ' };

	public Scanner()
	{
		s = new string[0];
		i = 0;
	}

	public string next()
	{
		if (i < s.Length) return s[i++];
		string st = Console.ReadLine();
		while (st == "") st = Console.ReadLine();
		s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
		i = 0;
		return next();
	}

	public int nextInt()
	{
		return int.Parse(next());
	}

	public long nextLong()
	{
		return long.Parse(next());
	}

	public double nextDouble()
	{
		return double.Parse(next());
	}
}