Problem:
Score : 300 points

Problem Statement

In Takahashi Kingdom, there is an archipelago of N islands, called Takahashi Islands.
For convenience, we will call them Island 1, Island 2, ..., Island N.

There are M kinds of regular boat services between these islands.
Each service connects two islands. The i-th service connects Island a_i and Island b_i.

Cat Snuke is on Island 1 now, and wants to go to Island N.
However, it turned out that there is no boat service from Island 1 to Island N, so he wants to know whether it is possible to go to Island N by using two boat services.

Help him.

Constraints

3 ≤ N ≤ 200 000

1 ≤ M ≤ 200 000

1 ≤ a_i < b_i ≤ N

(a_i, b_i) \neq (1, N)

If i \neq j, (a_i, b_i) \neq (a_j, b_j).

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

If it is possible to go to Island N by using two boat services, print POSSIBLE; otherwise, print IMPOSSIBLE.

Sample Input 1

3 2
1 2
2 3

Sample Output 1

POSSIBLE

Sample Input 2

4 3
1 2
2 3
3 4

Sample Output 2

IMPOSSIBLE

You have to use three boat services to get to Island 4.

Sample Input 3

100000 1
1 99999

Sample Output 3

IMPOSSIBLE

Sample Input 4

5 5
1 3
4 5
2 3
2 4
1 4

Sample Output 4

POSSIBLE

You can get to Island 5 by using two boat services: Island 1 -> Island 4 -> Island 5.

Solution in Pascal (FPC 2.6.2) (judge verdict: Accepted)

program V1004;
 var
  a:array[0..200001,0..1] of longint;
  i,m,n,x,y,u:longint;
 begin
  readln(n,m);
  fillchar(a,sizeof(a),0);
  a[1,0]:=1;
  a[n,1]:=1;
  for i:=1 to m do
   begin
    readln(x,y);
    if x=1 then inc(a[y,0]);
    if y=n then inc(a[x,1]);
   end;
  u:=0;
  for i:=1 to n do
   if (a[i,0]>0) and (a[i,1]>0) then u:=1;
  if u=1 then writeln('POSSIBLE')
         else writeln('IMPOSSIBLE');
 end.