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 ec12;
var 
	head,last,next,side:array[1..400002] of longint;
	n,m,i,j,p,q,tot,x,y:longint;
procedure add(x,y:longint);
begin 
	inc(tot);
	if head[x]=-1 then 
	begin 
		last[x]:=tot;
		next[tot]:=-1;
		side[tot]:=y;
		head[x]:=tot;
	end
	else
	begin 
		next[last[x]]:=tot;
		next[tot]:=-1;
		side[tot]:=y;
		last[x]:=tot;
	end;
end;
begin
	readln(n,m);
	for i:=1 to n do 
	head[i]:=-1;
	tot:=0;
	for i:=1 to m do 
	begin 
		readln(x,y);
		add(x,y);
	end;
	p:=head[1];
	while p>0 do 
	begin 
		q:=head[side[p]];
		while q>0 do 
		begin 
			if side[q]=n then 
			begin 
				writeln('POSSIBLE');
				halt;
			end;
			q:=next[q];
		end;
		p:=next[p];
	end;
	writeln('IMPOSSIBLE');
end.