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::collections;
use std::error::Error;
use std::io;
use std::process;

fn main() {
    if let Err(_) = run() {
        process::exit(1);
    }
}

fn run() -> Result<(), Box<Error>> {
    let mut nm = String::new();
    io::stdin().read_line(&mut nm)?;
    let nm: Vec<&str> = nm.trim().split(" ").collect();
    let n: i32 = nm[0].parse()?;
    let m: i32 = nm[1].parse()?;
    let mut adjs1 = collections::HashSet::new();
    let mut adjsn = collections::HashSet::new();
    for _ in 0..m {
        let mut ab = String::new();
        io::stdin().read_line(&mut ab)?;
        let ab: Vec<&str> = ab.trim().split(" ").collect();
        let a: i32 = ab[0].parse()?;
        let b: i32 = ab[1].parse()?;
        if a == 1 {
            adjs1.insert(b);
        }
        if a == n {
            adjsn.insert(b);
        }
        if b == 1 {
            adjs1.insert(a);
        }
        if b == n {
            adjsn.insert(a);
        }
    }
    for x in adjs1 {
        if adjsn.contains(&x) {
            println!("POSSIBLE");
            return Ok(());
        }
    }
    println!("IMPOSSIBLE");
    Ok(())
}