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 (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

func out(x ...interface{}) {
	fmt.Println(x...)
}

var sc = bufio.NewScanner(os.Stdin)

func getInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func getString() string {
	sc.Scan()
	return sc.Text()
}

func f(b, n int) int {
	if b > n {
		return n
	}
	return f(b, n/b) + n%b
}

func main() {
	sc.Split(bufio.ScanWords)

	N := getInt()
	S := getInt()

	ans := -1
	if N == S {
		ans = N + 1
		fmt.Println(ans)
		return
	}
	m := int(math.Sqrt(float64(N))) + 1
	for b := 2; b < m; b++ {
		if f(b, N) == S {
			ans = b
			break
		}
	}
	div := N - S
	if ans == -1 {
		for p := 1; p < m; p++ {
			if div%p != 0 {
				continue
			}
			b := div/p + 1
			if b < m {
				continue
			}
			if (f(b, N) == S) && (b > S-p) && (b < ans) {
				ans = b
				break
			}
		}
	}

	fmt.Println(ans)
}