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;


class A {
    public long f(long b, long n){
        long ans = 0;
        if(n<b){
            ans = n;
        } else {
            ans = f(b,n/b)+n%b;
        }
        return ans;
    }
    public long calc(long n, long s){
        
        if(n<s) return -1;
        if(n==s) return n+1;
        long up = (long)Math.Sqrt(n)+1;
        for(long i=2;i<up;i++){
            if(s==f(i,n)){
                return i;
            }
        }
        
        up = Math.Min(up, s);
        for(long i=1;i<up+1;i++){
            if( (i+n-s)%i==0){
                long b = (i+n-s)/i;
                long q = s-i;
                if(0<=q && q<b){
                    return (i+n-s)/i;
                }
            } 
        }
        return -1;
        
    }
}

class Program {
    static void Main(string[] args){
        A a = new A();
        long n = long.Parse(Console.ReadLine());
        long s = long.Parse(Console.ReadLine());
        Console.WriteLine(a.calc(n,s));
    }
}