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 JavaScript (node.js v5.12) (judge verdict: Accepted)

function Main(s) {
	s = s.split("\n").map(a => parseInt(a));
	const n = s[0];
	s = s[1];
	const sn = Math.ceil(Math.sqrt(n));
	if(s === n){console.log(n+1);return;}
	for(var b = 2; b < sn; b++){
		if(s === f(b, n)){
          console.log(b);
          return;
        }
	}
	var p = Math.floor((n - s) / (sn - 1));
	for(; p > 0; p--){
		b = Math.floor((n - s) / p + 1);
		if(s === f(b, n)){
          console.log(b);
          return;
        }
	}
	
	console.log(-1);
}
function f(b, n){
	if(n < b) return n;
	return f(b, Math.floor(n / b)) + n % b;
}

Main(require("fs").readFileSync("/dev/stdin", "utf8").trim());