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;
class Program{
	static void Main(){
		long n=long.Parse(Console.ReadLine());
		long s=long.Parse(Console.ReadLine());
		long ans=n-s+1;
		if(n==s){ans=n+1;}
		else if(s>n/2+(n%2)){ans=-1;}
		else{
			int r=(int)Math.Sqrt(n);
			for(int i=2;i<=r;i++){
				if(fu(i,n)==s){ans=i;break;}
				else if((n-s)%i==0&&fu((n-s)/i+1,n)==s){ans=(n-s)/i+1;}
			}
		}
		Console.WriteLine("{0}",ans);
	}
	static long fu(long b,long n){return n<b?n:fu(b,n/b)+n%b;}
}