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;
using System.Collections.Generic;
class Solve{
    public long n;
    public long s;
    public Solve(){}
    public static int Main(){
        new Solve().Calc();
        return 0;
    }
    void Calc(){
        getinput();
        if(n <= s){
            if(n == s){
                Console.WriteLine(n+1);
            }
            else{
                Console.WriteLine(-1);
            }
        }
        else{
            long i;
            for(i=2;i*i<=n;i++){
                long sum = 0;
                long a = n;
                while(a > 0){
                    sum += a%i;
                    a /= i;
                }
                if(sum == s){
                    Console.WriteLine(i);
                    return;
                }
            }
            if(i > s)
                i = s;
            for(;i>=1;i--){
                if((n-s+i)%i == 0 && (n-s+i)/i > i && s-i < (n-s+i)/i){
                    Console.WriteLine((n-s+i)/i);
                    return;
                }
            }
            Console.WriteLine(-1);
        }
    }
    void getinput(){
        n = Int64.Parse(Console.ReadLine());
        s = Int64.Parse(Console.ReadLine());
    }    
}