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: Accepted)

n, m = map(int, input().split())
# 素因数分解
from collections import defaultdict


def divide(n):  # unsort
    ans = []
    for i in range(1, int(n ** 0.5) + 1):
        if n % i == 0:
            ans.append(i)
            if n // i == i:
                continue
            ans.append(n // i)
    return ans


ans = 1
soin = divide(m)
soin.sort(reverse=True)
for num in soin:
    if num * n <= m:
        ans = num
        break

print(ans)