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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

N = int(input())
S = int(input())
import math

def Base_10_to_n(X, nn):
    X_dumy = X
    out = ''
    total = 0
    while X_dumy > 0:
        out = str(X_dumy % nn)+out
        total = X_dumy % nn + total
        X_dumy = int(X_dumy / nn)
    return total

#print(Base_10_to_n(119,11))
for b in range(N):
#  N_converted = list(Base_10_to_n(N, b+1))
#  N_converted_int = [int(s) for s in N_converted]
#  if sum(N_converted_int) == S:
#    print('Yes')
  if Base_10_to_n(N, b+2) == S:
    print(b+2)
    exit()

print(-1)