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

S = list(map(int,input().split()))
N = S[0]
M = S[1]
div = list()
z = math.sqrt(M)
z = math.ceil(z)

for x in range(1,z):
    if M % x == 0:
        div.append(x)
        div.append(M//x)
div.append(M)
div.append(N)

sorted_div = sorted(div)
n = sorted_div.index(N)

y =sorted_div[n+1]

ans = M // y

print(ans)