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: Wrong Answer)

import java.util.*;
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        long s = sc.nextLong();
        if (s == n) {
            System.out.println(n + 1);
            return;
        }
        for (long i = 2; i * i <= n; i++) {
            if (solve(n, s, i)) {
                System.out.println(i);
                return;
            }
        }
        boolean ok = false;
        long ans = 1000000000000L;
        for (long p = 1; p * p < n; p++) {
            long b = (n - s) / p + 1;
            // System.out.println("b = " + b);
            if (!(b * b > n && b < n)) {
                continue;
            }
            if (solve(n, s, b)) {
                ans = Math.min(ans, b);
                ok = true;
            }
        }
        if (!ok) {
            System.out.println(-1);
            return;
        }
        System.out.println(ans);
    }
    public static boolean solve(long n, long s, long num) {
        long ans = 0;
        while (n > 0) {
            ans += n % num;
            n /= num;
        }
        if (ans == s) {
            return true;
        }
        return false;
    }
}