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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;
import java.util.List;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Set;
import java.util.Map;
import java.util.HashMap;

public class Main {
    public static void main(String[] args) throws Exception {
        // Here your code !
        Scanner sc = new Scanner(System.in);
        long N = sc.nextLong();
        long S = sc.nextLong();
        long result = -1;
        String x = String.valueOf(N);
        int ketaN = x.length();
        String y = String.valueOf(S);
        int ketaS = y.length();
        
        int start = 2;
        if(ketaS>1){
            start = (int)Math.pow(10,ketaS-2);
        }
        
        for(long i=start;i<=N+1;i++){
            long b=i;
            long n = N;
            long sum = 0;
            while(b<=n){
                sum += n%b;
                n = n/b;
                if(sum > S){
                    break;
                }
            }
            sum += n%b;
            if(sum == S){
                result = i;
                break;
            }
        }
        
        System.out.println(result);
        
    }
}