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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
int64_t n, s, b = 100000000000;
int64_t calc(int64_t b, int64_t n)
{
    if(n < b) return n;
    return calc(b, n/b) + (n % b);
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin>>n>>s;
    if(n == s)
    {
        cout<<n + 1<<endl;
        return 0;
    }
    if(s == 1)
    {
        cout<<n<<endl;
        return 0;
    }
    for(int i = 2; i <= sqrt(n); ++i)
    {
        if(s == calc(i,n))
        {
            cout<<i<<endl;
            return 0;
        }
    }

    for(int i = sqrt(n-s); i >= 1; i--)
    {
        if( (n - s) % i == 0){
            int64_t t = ((n - s)/i + 1);
            if(s == calc(t,n)){
                b = min(b,t);
            }
        }
    }
        if(b != 100000000000)
            cout<<b<<endl;
        else cout<<-1<<endl;
    return 0;
}