Problem:
Score : 400 points

Problem Statement

You are given integers N and M.

Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

N \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.

Sample Input 1

3 14

Sample Output 1

2

Consider the sequence (a_1, a_2, a_3) = (2, 4, 8). Their greatest common divisor is 2, and this is the maximum value.

Sample Input 2

10 123

Sample Output 2

3

Sample Input 3

100000 1000000000

Sample Output 3

10000

Solution in Python (3.4.3) (judge verdict: Runtime Error)

def enum_divisors(n, reverse=False):
    divisors = []
    for i in range(1, int(math.sqrt(n)) ):
        if n % i == 0:
            divisors.append(i)
            if i != 1 and i * i != n:
                divisors.append(n//i)
    return sorted(divisors, reverse=reverse)

divisors = enum_divisors(M, reverse=True)
divisors = filter(lambda x: x <= M//N, divisors)

for cand in divisors:
    if M % cand == 0:
        print(cand)
        exit()