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 Ruby (2.3.3) (judge verdict: Accepted)

require 'prime'
N, M = gets.split.map(&:to_i)

primes = Prime.prime_division(M)

num = 1
primes.each do |pr, n|
    num *= n+1
end
divs = []
num.times do |i|
    prod = 1
    primes.each do |pr, n|
        prod *= pr ** (i % (n+1))
        i /= n+1
    end
    divs.push(prod)
end

puts divs.select{|d| d*N <= M}.max