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"
  "os"
  "strconv"
  "fmt"
  "math"
)

var reader = bufio.NewReaderSize(os.Stdin, 1000000)
var writer = bufio.NewWriter(os.Stdout)
func NextLine() string {
  var line, buffer []byte
  var isPrefix bool = true
  var err error
  for isPrefix {
    line, isPrefix, err = reader.ReadLine()
    if err != nil { panic(err) }
    buffer = append(buffer, line...)
  }
  return string(buffer)
}
func NextInt() int {
  var n int
  n, _ = strconv.Atoi(NextLine())
  return n
}
func Write(s interface{}) {
  fmt.Fprintln(writer, s)
}
func Output() {
  _ = writer.Flush()
}

func f(b, n int) int {
  cnt := 0
  for n > 0 {
    cnt += n % b
    n /= b
  }
  return cnt
}

func main() {
  n := NextInt()
  s := NextInt()
  sqrt := int(math.Sqrt(float64(n)))
  F := make([]int, sqrt + 1)
  ans := -1
  for b := 2; b < sqrt + 1; b++ {
    if F[b] < 0 { continue }
    fbn := f(b, n)
    if fbn == s {
      ans = b
      break
    }
    if fbn > s {
      k := fbn
      for k < sqrt + 1 {
        F[k] = -1
        k *= b
      }
    }
  }
  if ans < 0 {
    b := n + 1
    for b1 := 1; b1 < sqrt; b1++ {
      b0 := s - b1
      if n < b0 { continue }
      if b0 < 0 { break }
      if (n - b0) % b1 > 0 { continue }
      _b := (n - b0) / b1
      if _b <= b0 { continue }
      if _b < b { b = _b }
    }
    if b < n + 1 { ans = b }
    if n == s { ans = n + 1 }
    if s == 1 { ans = n }
  }
  Write(ans)
  Output()
}