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 (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<stdio.h>

#define min(a, b) ((a) < (b) ? (a) : (b))

long long f(long long b, long long n){
  long long ret = 0;
  while(n){
    ret += n % b;
    n /= b;
  }
  return ret;
}

int main(){
  long long n, s;
  scanf("%lld%lld", &n, &s);
  
  long long ans = -1;
  if(n == s) ans = n + 1;
  for(long long b = 2; b * b <= n; ++b){
    if(f(b, n) == s){
      ans = b;
      break;
    }
  }
  
  for(long long a1 = 1; a1 <= s && a1 * a1 <= n; ++a1){
    long long a0 = s - a1;
    
    if(a0 * a0 > n || (n - a0) % a1) continue;
    
    long long b = (n - a0) / a1;
    if(a0 >= b || a1 >= b) continue;
    
    if(ans >= 0) ans = min((n - a0) / a1, ans);
    else ans = (n - a0) / a1;
  }
  
  printf("%lld\n", ans);
  
  return 0;
}