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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

@NM = split(" ", <STDIN>);
@ab;
for (0..$NM[1]) {
    @tmp = split(" ", <STDIN>);
    push @ab, @tmp;
}

if (!(grep { $_ == 1} @ab) || !(grep { $_ == $NM[0]} @ab)) {
    print "IMPOSSIBLE";
    exit();
}

@_ab = @ab;
$k = ($NM[1] * $NM[1]-1) / 2; # 組み合わせの個数 $NM[1]C2
for (0..$k) {
    @ab = @_ab;
    $count = 0;
    $now = $NM[0];
    for my $n (@ab) {
        if ($n == $now) {
            if ($count % 2) {
                $now = $ab[$count-1];
                delete($ab[$count]);
                delete($ab[$count-1]);
                last;
            } else {
                $now = $ab[$count+1];
                delete($ab[$count]);
                delete($ab[$count+1]);
                last;
            }
        }
        $count++;
    }
    
    $_now = $now;
    $count = 0;
    for my $n (@ab) {
        if ($n == $now) {
            if ($count % 2) {
                $now = $ab[$count-1];
                if ($now == 1) {
                    print "POSSIBLE";
                    exit();
                }
                $now = $_now;
            } else {
                $now = $ab[$count+1];
                if ($now == 1) {
                    print "POSSIBLE";
                    exit();
                }
                $now = $_now;
            }
        }
        $count++;
    }
}

print "IMPOSSIBLE";