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)

extern crate core;

use std::io::{self, Read};

fn main() {
    let mut input = String::new();
    io::stdin().read_to_string(&mut input).unwrap();
    let output = run(input.trim().to_string());
    println!("{}", output);
}

fn run(input: String) -> String {
    let n = input
        .split_whitespace()
        .nth(0)
        .unwrap()
        .parse::<usize>()
        .unwrap();

    let goal = n - 1;

    let list = input
        .split("\n")
        .skip(1)
        .flat_map(|x| {
            let l = x.split_whitespace()
                .map(|x| x.parse::<usize>().unwrap() - 1)
                .collect::<Vec<_>>();
            vec![(l[0], l[1]), (l[1], l[0])]
        })
        .collect::<Vec<_>>();

    let mut nodes = Vec::new();
    for _ in 0..n {
        nodes.push(vec![]);
    }

    for (a, b) in list.into_iter() {
        nodes[a].push(b);
    }

    for &route in &nodes[0] {
        if route == goal {
            return "POSSIBLE".to_string();
        }

        for &route2 in &nodes[route] {
            if route2 == goal {
                return "POSSIBLE".to_string();
            }
        }
    }

    "IMPOSSIBLE".to_string()
}

macro_rules! tests {
    ($($name:ident: $input:expr=>$output:expr,)*) => {
        mod tests {
            $(
                #[test]
                fn $name() {
                    assert_eq!(super::run($input.to_string()), $output.to_string());
                }
            )*
        }
    }
}

tests! {
    test1: "3 2
1 2
2 3" => "POSSIBLE",
    test2: "4 3
1 2
2 3
3 4" => "IMPOSSIBLE",
    test3: "100000 1
1 99999" => "IMPOSSIBLE",
    test4: "5 5
1 3
4 5
2 3
2 4
1 4" => "POSSIBLE",
}