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: Time Limit Exceeded)

main=getLine>>=print.solve.map read.words
solve [n,m]
 | n==1 = m
 | otherwise = go divs
 where
 go (d:divs)
  | d*n<=m = d
  | otherwise = go divs
 divs = (map(div m).reverse)divs++(f.floor.sqrt.fromIntegral)m
 f 1 = [1]
 f d
  | m`mod`d==0 = d:f(d-1)
  | otherwise = f(d-1)