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: Time Limit Exceeded)

use std::io;
use std::io::Read;

fn main() {
    let mut input = String::new();
    io::stdin().read_to_string(&mut input).unwrap();
    let input : Vec<&str> = input.trim().split('\n').collect();
    let l1 : Vec<&str> = input[0].split(' ').collect();
    let n = l1[0];

    let mut res = Vec::new();
    for l in input[1..].iter() {
        let l : Vec<&str> = l.split(' ').collect();
        if l[0] == "1" {
            match res.iter().find(|&&s| s == l[1]) {
                None => res.push(l[1]),
                Some(_) => {
                    println!("POSSIBLE");
                    std::process::exit(0);
                }
            }
        } else if l[1] == n {
            match res.iter().find(|&&s| s == l[0]) {
                None => res.push(l[0]),
                Some(_) => {
                    println!("POSSIBLE");
                    std::process::exit(0);
                }
            }
        }
    }

    println!("IMPOSSIBLE");
}