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;

#define forn(i, n) for (ll i = 0; i < (ll) (n); ++i)
#define sz(a) static_cast<int>((a).size())
#define pb emplace_back
#define mp make_pair
#define endl '\n'
#define f first
#define s second

#ifdef SEREZHKA
#define dbg(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
#else
#define dbg(...)
#endif

template<typename T>
void _dbg(const char* _s, T _h) { cerr << _s << " = " << _h << "\n"; }

template<typename T, typename... Ts>
void _dbg(const char*_s, T _h, Ts... _t) {
    int _b = 0;
    
    while (((_b += *_s == '(') -= *_s == ')') != 0 || *_s != ',')
        cerr << *_s++;
    
    cerr << " = " << _h << ",";
    _dbg(_s + 1, _t...);
}

using ll = long long;

const ll INF = static_cast<ll>(1e9) + 7ll;
const ll LINF = INF * INF;
const int MAXN = static_cast<int>(4e2) + 17;

ll n, s;

bool read() {
    if (!(cin >> n >> s))
        return false;

    return true;
}

ll f(ll b, ll n) {
    ll sum = 0;
    for (; n > 0; sum += n % b, n /= b) { }
    return sum;
}

void solve() {
    ll ans = INF * INF;

    for (ll b = 2; b * b <= n; ++b)
        if (f(b, n) == s)
            ans = min(ans, b);

    if (n - s > 0) {
        ll t = n - s;

        for (ll d = 1; d * d <= t; ++d)
            if (t % d == 0) {
                if (f(d + 1, n) == s) ans = min(ans, d + 1);
                if (f(t / d + 1, n) == s) ans = min(ans, t / d + 1);
            }
    }

    cout << (ans == INF * INF ? -1 : ans) << endl;
}

int main() {
    cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    
    while (read())
        solve();
    
    return 0;
}