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 OCaml (4.02.3) (judge verdict: Accepted)

let n, m, ans = Scanf.scanf "%d %d" @@ fun a b -> a, b, ref 0
let f g n = let rec f i = if i * i <= n then (if n mod i = 0 then (g i; if i <> n / i then g (n / i)); f (i + 1)) in f 1
let g d = if m / d >= n then ans := max !ans d
let _ = f g m; Printf.printf "%d\n" !ans