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;

long long f(long long b, long long n) {
    if (b <= 1) return -1;
    if (n < b) return n;
    else return f(b, n / b) + n % b;
}
int main() {
    long long n, s;

    scanf("%lld%lld", &n, &s);
    long long res = 1e13 + 1;

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

    if (s > n) {
        cout << -1 << endl;
        return 0;
    }


    for (long long b = 2; b * b < n; ++b) {
        if (f(b, n) == s) res = min(res, b);
    }

    for (long long p = 1; p * p < n; ++p) {
        long long r = s - p;
        long long b = (n - r) / p;
        if (f(b, n) == s) res = min(res, b);
    }

    if (res == 1e13 + 1) cout << -1 << endl;
    else cout << res << endl;


    return 0;
}