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)

type mang=array[0..1000005] of longint;
var h,a,x,y:mang;
    n,m,dem:longint;
    kt:boolean;
procedure nhap;
var i:longint;
begin
   read(n,m);
   for i:=1 to m do
      begin
      read(x[i],y[i]);
      inc(h[x[i]]);
      end;

   for i:=1 to n do
      h[i]:=h[i-1]+h[i];

   for i:=1 to m do
      begin
      a[h[x[i]]]:=y[i];
      dec(h[x[i]]);
      end;
   h[n+1]:=m;

end;

procedure DFS(i:Longint);
var j:longint;
begin
   if kt=true then exit;
   for j:=h[i]+1 to h[i+1] do
      begin
         dem:=dem+1;
         if (a[j]=n ) and (dem=2) then
            begin
            kt:=true;
            exit;
            end;
         if dem<2 then DFS(a[j]);
         dem:=dem-1;
      end;
end;

procedure xuly;
begin
   kt:=false;
   dem:=0;
   DFS(1);
end;

procedure xuat;
begin
   if kt=true then write('POSSIBLE')
      else write('IMPOSSIBLE');
end;

begin

   nhap;
   xuly;
   xuat;

end.