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)

N,M = readline.split.map(&:to_i)

require 'prime'
primes = Prime.prime_division(M)

$max = 1
def find_largest(primes, i, x)
  if i>=primes.size
    $max = x if x > $max
  else
    b,emax = primes[i]
    #pp primes, i, emax
    (0..emax).each do |e|
      div = x * (b**e)
      #pp "div: #{div}, i:#{i} e:#{e}"
      break if div > M/N
      find_largest(primes, i+1, div)
    end
  end
end

find_largest(primes, 0, 1)
puts $max