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: Wrong Answer)

N,M=gets.chomp.split(" ").map { |e| e.to_i  }

const = 0
val = Math.sqrt(M)

if M%N == 0
  puts M/N
  exit
end
a=[]
indx = 0
for i in 1..val do
  if M % i == 0
    a[indx] = i
    a[indx+1] = M/i
    indx += 2
  end
end

for i in a do
  if  M % i == 0 && N*i <= M
     const = i
  end
end

puts const