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 Rust (1.15.1) (judge verdict: Accepted)

fn get_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().to_string()
}

fn reads<T>() -> Vec<T>
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().split(' ').map(|x| x.parse().unwrap()).collect()
}

fn main() {
    let nm = reads();
    let mut xs = vec![vec![]; nm[0]];

    for _ in 0..nm[1] {
        let ab: Vec<usize> = reads();

        let a = ab[0] - 1;
        let b = ab[1] - 1;

        xs[a].push(b);
        xs[b].push(a);
    }

    let mut res = false;
    let mut ss = vec![];

    for &x in &xs[0] {
        if x == nm[0] - 1 {
            res = true;
            break;
        }
        else {
            ss.push(x);
        }
    }

    if !res {
        'outer:
        for s in ss {
            for &x in &xs[s] {
                if x == nm[0] - 1 {
                    res = true;
                    break 'outer;
                }
            }
        }
    }


    println!("{}POSSIBLE",
        if res {
            ""
        }
        else {
            "IM"
        }
    );
}