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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

def main():
    N, M = (int(i) for i in input().split())

    def gcd(x, y):
        if y == 0:
            return x
        while y != 0:
            x, y = y, x % y
        return x

    if M % N == 0:
        return print(M//N)

    ans = 1
    for i in range(2, M//N+1)[::-1]:
        cur = gcd(i, M - i*(N-1))
        if cur == 1:
            continue
        else:
            ans = max(ans, cur)
            break
    print(ans)


if __name__ == '__main__':
    main()