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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local n,m=io.read("n","n")
if m%n==0 then
    print(m//n)
else
    local d={}
    for i=1,math.sqrt(m) do
        if m%i==0 then
            table.insert(d,i)
            table.insert(d,m//i)
        end
    end
    table.sort(d)

    local max=0
    for _,v in pairs(d) do
        if v*n<=m then
            max=math.max(max,v)
        end
    end
    print(max)
end