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)

import math
n, m = map(int, input().split())
fact = []
ans = 1
MAX = int(math.sqrt(m)) + 1
for i in range(1, MAX):
    if m % i == 0:
        fact.append(i)
        if i != m // i:
            fact.append(m//i)
fact.sort()
for x in fact:
    if m < n * x:
        break
    ans = x
print(ans)