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 (3.8.2) (judge verdict: Accepted)

n,m = map(int,input().split())

def f(m):
    d = []
    r = int(m**0.5)
    for i in range(1,r+1):
        if m % i == 0:
            d.append(i)
            d.append(m//i)
    d.sort(reverse = 1)
    return d

d = f(m)
for x in d:
    p = m//x
    #print(x,p)
    #if n <= p and p % n != 0:
    if n <= p:
        print(x)
        exit()