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;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = Long.parseLong(sc.next());
		long s = Long.parseLong(sc.next());

		long lower = 0;
		long upper = 0;
		for(int i = 10; i <= Math.pow(10, 11); i *= 10) {
			long temp = function(i, n);
			if(temp >= s) {
				lower = i / 10;
				upper = i;
				break;
			}
		}


		boolean flag = false;
		for(int b = 2; b < Math.pow(10, 11); b++) {
			if(function(b, n) == s) {
				System.out.println(b);
				flag = true;
				break;
			}
		}

		if(!flag) System.out.println(-1);
	}

	public static long function(long b, long n) {
		if(n < b) {
			return n;
		}else {
			return function(b, (long)(n/b))+(n%b);
		}
	}

//	public static long sumDigit(long value) {
//		if(value <= 9) {
//			return value;
//		}else {
//			double divTen = value / 10;
//			long intValue = (long)divTen;
//			int digit = (int)((divTen - intValue) * 10);
//			return sumDigit(intValue) + digit;
//		}
//	}

}