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 Ruby (2.3.3) (judge verdict: Accepted)

n, s = 2.times.map {gets.to_i}

bs = Math.sqrt(n).ceil
BIG = 10**12
ans = BIG

(2..bs).each do |i|
    n1 = n
    sum = 0
    while n1 > 0
        sum += n1 % i
        n1 /= i
    end
    if sum == s
        puts i
        exit
    end
end

(1..bs).each do |ud|
    ld = s - ud
    next if ld < 0
    next if (n - ld) % ud > 0
    b = (n - ld) / ud
    if b > ld && b > ud
        ans = [ans, b].min
    end
end

if n == s
    ans = [ans, n+1].min
end

puts ans == BIG ? -1 : ans