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: Time Limit Exceeded)

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

namespace ConsoleApplication17
{
    class Program
    {
        static void Main(string[] args)
        {
            //(n < b) のとき f(b,n) = n
            //(n >= b)のとき f(b,n) = f(b,floor(n/b)) + (n mod b)
            //
            //f(b,n) = sを満たす様なbの最小値を出力する
            //

            UInt64 n = UInt64.Parse(Console.ReadLine());
            UInt64 s = UInt64.Parse(Console.ReadLine());

            Console.WriteLine(solve(n, s).ToString());
            Console.ReadLine();
        }

        static Int64 solve(UInt64 n, UInt64 s)
        {

            if (s == n) return (Int64)(n + 1);
            UInt64 b = 2;
            while (b <= n)
            {
                UInt64 ans = 0;
                if (Func(b, n, s, ref ans))
                {
                    if (ans == s) return (Int64)b;
                }
                b++;
            }
            return -1;
        }

        static bool Func(UInt64 b, UInt64 n, UInt64 target, ref UInt64 modPool)
        {
            if (n < b)
            {
                modPool += n;
                return true;
            }

            modPool += (n % b);
            if (modPool > target) return false;

            return Func(b, (UInt64)Math.Floor((double)(n / b)), target, ref modPool);
        }
    }
}