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: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <stdbool.h>

#define lli long long int
#define min(a,b) ((a)<(b)?(a):(b))
#define max(a,b) ((a)>(b)?(a):(b))

lli f(lli b,lli n){
	if(n < b){
		return n;
	}
	return f(b,n / b) + n % b;
}
bool judge(lli b,lli n,lli s){
	return f(b,n) == s;
}


int main(void){
	lli i;
	lli n,s;
	lli sqrtn;
	lli b;
	scanf("%lld",&n);
	scanf("%lld",&s);
	if(s==n){
		printf("%lld\n", n+1);
		return 0;
	}
	sqrtn = (lli)sqrt((double)n);
	for(i=2;i<=sqrtn;i++){
		if(judge(i,n,s)){
			printf("%lld\n", i);
			return 0;
		}
	}
	for(i=sqrtn;i>=1;i--){
		b = (n - s) / i + 1;
		if(b <= 1){
			continue;
		}
		if(judge(b,n,s)){
			printf("%lld\n", b);
			return 0;
		}
	}
	printf("%d\n", -1);
	return 0;
}