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;

using ll = long long;

bool Equal(ll n, ll b, const ll s) {
    ll sum = 0;
    while (n) {
        sum += n % b;
        n /= b;
    }
    return sum == s;
}

ll Solve() {
    ll n, s;
    cin >> n >> s;
    if (n == s) return n + 1;
    else if (n < s) return -1;
    else if (s == 1) return n;

    for (ll b = 2; b * b <= n; ++b)
        if (Equal(n, b, s)) return b;

    ll NS = n - s, res = n;
    for (ll p = 2; p * p <= NS; ++p) {
        if (NS % p != 0) continue;

        ll b1 = p + 1, b2 = NS / p + 1;
        if (Equal(n, b1, s)) res = min(res, b1);
        if (Equal(n, b2, s)) res = min(res, b2);
    }

    return (res == n ? -1 : res);
}

int main() {
    cin.tie(0); ios::sync_with_stdio(false);

    cout << Solve() << endl;

    return 0;
}