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)

use std::io;
use std::process;

macro_rules! parse_line {
    ($($t: ty),+) => ({
        let mut a_str = String::new();
        io::stdin().read_line(&mut a_str).expect("read error");
        let mut a_iter = a_str.split_whitespace();
        (
            $(
            a_iter.next().unwrap().parse::<$t>().expect("parse error"),
            )+
        )
    })
}

fn possible() {
    println!("POSSIBLE");
    process::exit(0);
}

fn main() {
    let size = 200000;
    let (N, M) = parse_line!(i32, i32);
    let mut linked_list: Vec<Vec<i32>> = Vec::with_capacity(size);

    for _ in 0..size + 1 {
        linked_list.push(Vec::new());
    }

    for _ in 0..M {
        let (a, b) = parse_line!(i32, i32);
        linked_list.get_mut(a as usize).unwrap().push(b);
        linked_list.get_mut(b as usize).unwrap().push(a);
    }

    for first in &linked_list[1] {
        if *first == N {
            possible();
        }

        for second in &linked_list[*first as usize] {
            if *second == N {
                possible();
            }
        }
    }
    println!("IMPOSSIBLE");
}