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: Accepted)

import math


def divisor(num):
    if num < 0:
        return [0,]
    elif num == 1:
        return [1,]
    else:
        divisor_list =[1,]
        for i in range(2, int(math.sqrt(num) + 1)):
            if num % i== 0:
                divisor_list.append(i)
        return divisor_list


N,M = map(int,input().split(' '))
P = M // N
divisor_list = divisor(M)

for i in reversed(range(len(divisor_list))):
    num = M // divisor_list[i]
    divisor_list.append(num)

for i in reversed(range(len(divisor_list))):
    if divisor_list[i] <= P:
        print(divisor_list[i])
        break