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: Runtime Error)

import Data.List

main :: IO ()
main = do
  [n,m] <- map read . words <$> getLine
  print $ solve n m

solve :: Int -> Int -> Int
solve n m = m `div` y
  where y = head $ filter (>=n) $ factors m

factors :: Int -> [Int]
factors n = [x | x <- primes n, n `mod` x == 0]

primes :: Int -> [Int]
primes n = 2 : eratos [3,5 .. n]
  where
    eratos [] = []
    eratos (p:xs) = p : eratos (xs \\ [p,3*p..n])