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 (5.3.2) (judge verdict: Accepted)

function input()
  local inp = io.read()
  local r={}
  string.gsub(inp,"(%S+)", function (v) table.insert(r,tonumber(v)) end)
  return r
end

local n,m
local inp = input()
n = inp[1]
m = inp[2]
local b={}
local cnt = 1
local i=1
while i*i<=m do
  if m%i==0 then
    b[cnt]=i
    cnt = cnt+1
    b[cnt]=m//i
    cnt = cnt+1
  end
  i=i+1
end
local res = 1
for i=1,cnt-1,1 do
  if b[i]*n<=m then
    res = math.max(res,b[i])
  end
end
print(res)