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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
  n,m,d,ans:longint;
function check(x:longint):boolean;
begin
  if (m div x)>=n then
  begin
    check:=true;
  end
  else
  begin
    check:=false;
  end;
end;
begin
  ans:=1;
  readln(n,m);
  for d:=1 to trunc(sqrt(m)) do
  begin
    if (m mod d)<>0 then
    begin
      continue;
    end;
    if check(d) then
    begin
      if d>ans then
      begin
        ans:=d;
      end;
    end;
    if check(m div d) then
    begin
      if (m div d)>ans then
      begin
        ans:=m div d;
      end;
    end;
  end;
  writeln(ans);
end.