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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

typedef long long int lli;

lli n, s;

vector<lli> divisors;

bool checkValid(lli n, lli s, lli b) {
	lli actual = 0;
	while(n) {
		actual += (n%b);
		n /= b;
	}
	return (actual == s);
}

int main() {
	ios_base::sync_with_stdio(false);

	cin >> n >> s;

	if(n < s) {
		cout << -1 << endl;
		return 0;
	} else if(n == s) {
		cout << n+1 << endl;
		return 0;
	}

	lli m = n - s;

	for(lli i = 1; i < (lli)(sqrt(m)+1.5); i++) {
		if(m%i == 0) {
			divisors.push_back(i);
			divisors.push_back(m/i);
		}
	}

	sort(divisors.begin(), divisors.end());

	for(lli d: divisors) {
		if(checkValid(n, s, d+1)) {
			cout << d+1 << endl;
			return 0;
		}
	}

	cout << -1 << endl;

	return 0;
}