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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)


enumDivisor x b
  | b<=1 = [1]
  | otherwise = f (min b (x`div`2)) where
      f 1 = [1]
      f n
        | x`mod`n==0 = n : f (n-1)
        | otherwise = f (n-1)

main = do
  [n,m] <- map read . words <$> getLine :: IO [Int]
  print.head $ enumDivisor m (m`div`n)