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)
DS = M.prime_division

def r(x,i, &f)
  if i == DS.size
    return f.call(x)
  end
  a,b = DS[i]
  (0..b).each{ |j|
    r(x*(a**j), i+1, &f)
  }
end

$ans = 1

r(1,0) { |x|
  #p x
  if M/x >= N
    $ans = [$ans, x].max
  end
}
p $ans