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 (2.7.1) (judge verdict: Accepted)

def divisors(n)
  b = Array.new
  for i in 1..((n**0.5))
    if n % i == 0
      b.push(i)
    end
  end
  len = b.length
  len.times{|i|
    if n/b[len-1-i] != b[len-1-i]
      b.push(n/b[len-1-i])
    end
  }
  b
end
n,m = gets.chomp.split(" ").map(&:to_i)
max = 1
divisors(m).each do |i|
  if (m - i*n) >= 0 && (m - i*n) % i == 0
    max = i if i > max
  end
end
puts max