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


public class AtCoder {
    static long n, s;
    static void Main() {
        n = long.Parse(Console.ReadLine());
        s = long.Parse(Console.ReadLine());
        if (s == n) {
            Console.WriteLine(n + 1);
            return;
        }
        int rootn = (int)Math.Sqrt(n);
       for(int b = 1; b < rootn; b++) {
            if (b >= 2) {
                if (function(b, n) == s) {
                    Console.WriteLine(b);
                    return;
                }
            }
            long bigb = ((n - s) / b) + 1;
            if (function(bigb, n) == s) {
                Console.WriteLine(bigb);
                return;
            }
        }
       
        Console.WriteLine(-1);
    }
    static long function(long b,long n) {
        if (n < b) {
            return n;
        }
        return function(b, n / b) + n % b;
    }

}