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: Wrong Answer)

import math

N, M = map(int, input().split())

# N = 100000
# M = 1000000000

def get_div_list(num):
    if num == 1:
        return [1]
    else:
        div_list = []
        div_list.append(1)
        div_list.append(num)
        for i in range(2, math.floor(math.sqrt(num))+ 1):
            if num % i == 0:
                div_list.append(i)
                div_list.append(num // i)
        list(set(div_list))
        return div_list


L = get_div_list(M)
L = [i for i in L if i * N <= M]
# print(L)


for i in L[::-1]:
    if (M - (N * i)) % i == 0:
        ans = i
        break

print(ans)