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: Accepted)

import Control.Arrow
import Data.List
import qualified Data.ByteString.Char8 as B

main :: IO ()
main = breads >>= print . solve 

solve :: [Int] -> Int
solve [n, m]
    | v == 0 = r
    | otherwise = calc [r, (r - 1)..1]
    where
        (r, v) = m `divMod` n 

        calc (ans : xs)
            | y > 0 = calc xs
            | x > n + 1 = ans
            | otherwise = calc xs
            where
                (x, y) = m `divMod` ans

breads :: IO [Int]
breads = unfoldr (\s -> second (maybe B.empty snd . B.uncons) <$> B.readInt s) <$> B.getLine