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: Time Limit Exceeded)

@memo = {}
def gcd(l, r)
  return @memo[[l,r].to_s] if @memo[[l,r].to_s]
  if l%r==0
    @memo[[l,r].to_s] = r
    return r
  end
  @memo[[r, l%r].to_s] = gcd(r, l%r)
end

n, m = gets.strip.split.map(&:to_i)

result = 0
current = m/n

(m/n).times do |num|
  diff = m%current
  tmp_result = gcd(current + diff, current)
  result = tmp_result if tmp_result > result
  current -= 1
end

p result