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<cmath>
#include<cstdio>
#include<iostream>
using namespace std;
typedef long long ll;
ll s,n,m;
ll f(ll b,ll n) {
    if(n<b) return n;
    else return f(b,n/b)+n%b;
}
int main() {
    cin>>n>>s;
    m=sqrt(n)+1;
    if(s>n){
        cout<<"-1"<<endl;
        return 0;
    }
    if(s==n){
        cout<<s+1<<endl;
        return 0;
    }
    for(int  i=2;i<=m;++i){
        if(f(i,n)==s){
            cout<<i<<endl;
            return 0;
        }
    }
    ll b,q,res=1e11;
    n-=s;
    for(ll p=1;p*p<=n;++p){
        if (n%p==0){
            b=n/p+1;
            q=s-p;
            if(q>=0&&b>=2&&q<b&&p<b) res=min(res,b);
        }
    }
    if(res=1e11) cout<<"-1\n";
    else cout<<res<<endl;
    return 0;
}