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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

def i1():
 return int(input())
def i2():
 return [int(i) for i in input().split()]
n=i1()
s=i1()
a=[]
import math
def f(b,n):
    if n<b:
       return n
    else:
       return f(b,n//b)+n%b
if s==n:
  print(n+1)
elif s>n:
  print(-1)
else:
  for i in range(2,int(math.sqrt(n))+1):
      if f(i,n)==s:
         a.append(i)
  for i in range(1,int(math.sqrt(n))+1):
      if n>=n/i+1-s/i>int(math.sqrt(n)):
         if f(n/i+1-s/i,n)==s:a.append(n/i+1-s/i)
  if len(a):print(int(min(a)))
  else:print(-1)