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 (2.7.6) (judge verdict: Accepted)

#coding: utf-8
import math

n,m = map(int,raw_input().split())

a = []
root_m = int(math.sqrt(m)) + 1
for i in range(1,root_m):
    if m%i == 0:
        a.append(m/i)
        if i >= n:
            print m/i
            exit()
for i in reversed(a):
    if m%i == 0:
        if i >= n:
            print m/i
            exit()
print "1"