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 {
  private static long split(long n, long k) {
    long sum = 0;
    while (n > 0) {
      sum += n % k;
      n /= k;
    }
    return sum;
  }

  private static long solve(long n, long s) {
    long k;
    for (k = 2; k*k <= n; k++) {
      if (split(n, k) == s) {
        return k;
      }
    }
    while (k <= n) {
      long a = n / k;
      long b = n % k;
      if ((a + b - s) % a == 0) {
        long dk = (a + b - s) / a;
        if (dk >= 0 && b - dk*a >= 0) {
          return k + dk;
        }
      }
      k = n / a + 1;
    }
    return -1;
  }

  public static void main(String[] args) {
    Scanner s = new Scanner(System.in);
    long nl = s.nextLong();
    long sl = s.nextLong();
    System.out.println(solve(nl, sl));
  }
}