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: Runtime Error)

#include <iostream>
#include <algorithm>
#include <cmath>

using namespace std;

typedef long long ll;

ll digit_sum(ll i, ll b)
{
    ll ans = 0;
    while (i > 0)
    {
        ans += i % b;
        i /= b;
    }
    return ans;
}

const ll INF = 10000000000000000LL;

int main()
{
    ll n, s;
    cin >> n >> s;

    ll ans = INF;

    if (n == s)
    {
        cout << n + 1 << endl;
    }
    else
    {
        for (ll b = 2; b * b < n; b++)
        {
            if (digit_sum(n, b) == s)
            {
                ans = min(ans, b);
            }
        }

        for (ll p = 1; p * p < n; p++)
        {
            const ll b = (n - s) / p + 1;
            if (digit_sum(n, b) == s) 
            {
                ans = min(ans, b);
            }
        }

        if (ans == INF)
        {
            cout << -1 << endl;
        } 
        else
        {
            cout << ans << endl;
        }
    }
}