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: Wrong Answer)

var     a,b,h,st:array[0..200005]of longint;
        n,m,dem:longint;

procedure nhap;
var i:longint;
begin
        readln(n,m);
        for i:=1 to m do
            begin
                readln(a[i],b[i]);
                inc(h[a[i]]);
            end;
end;

procedure swap(var g,h:longint);
var temp:longint;
begin
        temp:=g;
        g:=h;
        h:=temp;
end;

procedure sort(l,r:longint);
var i,j,mid:longint;
begin
        i:=l;
        j:=r;
        mid:=a[(l+r) div 2];
        repeat
            while a[i]<mid do inc(i);
            while a[j]>mid do dec(j);
            if not(i>j) then
                begin
                    swap(a[i],a[j]);
                    swap(b[i],b[j]);
                    inc(i);
                    dec(j);
                end;
        until i>j;
        if i<r then sort(i,r);
        if l<j then sort(l,j);
end;

procedure xuli;
var     i,j:longint;
begin
        for i:=1 to 200005 do
                h[i]:=h[i-1]+h[i];
        sort(1,m);

        for i:=h[1] to h[2]-1 do
            begin
                if b[i]<>n then
                    begin
                        inc(dem);
                        st[dem]:=b[i];
                    end;
            end;
        if dem=0 then writeln('IMPOSSIBLE')
        else

            begin
                for i:=1 to dem do
                    for j:=h[st[dem]] to h[st[dem]+1] do
                        begin
                            if (b[j]=n) and (a[j]=st[dem]) then
                                begin
                                    writeln('POSSIBLE');
                                    halt
                                end;
                        end;
                writeln('IMPOSSIBLE');
            end;
end;

begin
       // assign(input,'at_c.inp');reset(input);
       // assign(output,'at_c.out');rewrite(output);
                nhap;
                xuli;
end.