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::stdin;
use std::collections::HashSet;

fn main(){
    let (n, m) = getpair();
    let mut foo: HashSet<usize> = HashSet::new();
    let mut bar: HashSet<usize> = HashSet::new();
    for _ in 0..m {
        let (a, b) = getpair();
        if a==1 {foo.insert(b);}
        if b==1 {foo.insert(a);}
        if a==n {bar.insert(b);}
        if b==n {bar.insert(a);}
    }

    let mut ans = false;

    for x in &foo {
        if bar.contains(x) {
            ans = true;
            break;
        }
    }

    println!("{}", if ans { "POSSIBLE" } else { "IMPOSSIBLE" });
}

#[allow(dead_code)]
fn getline() -> String {
    let mut s = String::new();
    match stdin().read_line(&mut s){
        Ok(_) => {s.trim().to_string()}
        Err(_) => String::new()
    }
}

#[allow(dead_code)]
fn getvec<T: std::str::FromStr>() -> Vec<T>{
    let line = getline();
    line.split_whitespace().filter_map(|x| x.parse().ok()).collect()
}

#[allow(dead_code)]
fn getpair() -> (usize, usize){
    let nm = getvec();
    (nm[0], nm[1])
}