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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
	"math"
)

const MAX = 50

type INT int64

func main() {
	solve()
}

func solve() {
	n, s := input()
	if n == s {
		fmt.Println(n + 1)
		return
	}
	for i := INT(2); i <= INT(math.Sqrt(float64(n))); i++ {
		if s == f(i, n) {
			fmt.Println(i)
			return
		}
	}
	for i := INT(1); i < INT(math.Sqrt(float64(n))); i++ {
		b := (n-s)/i + 1
		if 2 <= b && s == f(b, n) {
			fmt.Println(b)
			return
		}
	}
	fmt.Println(-1)
	return
}

func input() (n, s INT) {
	fmt.Scan(&n)
	fmt.Scan(&s)
	return n, s
}

func f(b, n INT) INT {
	if n < b {
		return n
	}
	return f(b, n/b) + n%b
}