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 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int main( int argc, char *argv[] )
{
  unsigned int n,b;
  unsigned int nn;
  unsigned int s;
  unsigned int a;
  int i;

  scanf( "%d%d", &n, &s );

  if( s == 1 ){
    printf( "%d\n", n );
    return 0;
  }
  if( n == s ){
    printf( "%d\n", n+1 );
    return 0;
  }

  for( b = 2; b < n; b ++ ){
    nn = n;
    a = 0;
    while( nn ){
      a += nn%b;
      nn = nn/b;
    }
    if( a == s ) break;
  }

//printf( "a %d b %d s %d n %d\n", a, b, s, n );  

  if( b == n ) b = -1;
  if( a > s ) b = -1;
  printf( "%d\n",b );

  return 0;
}