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::collections::VecDeque;

fn main() {
    let stdin = io::stdin();
    let mut buf = String::new();
    stdin
        .read_line(&mut buf)
        .expect("ERROR Can't read array size");
    let v: Vec<usize> = buf.split_whitespace()
        .map(|n| n.parse().unwrap())
        .collect();
    let n = v[0];
    let m = v[1];
    let mut graph: Vec<Vec<usize>> = Vec::with_capacity(n);
    for _ in 0..n {
        graph.push(Vec::new());
    }
    for _ in 0..m {
        let mut buf = String::new();
        stdin
            .read_line(&mut buf)
            .expect("ERROR Can't read array size");
        let v: Vec<usize> = buf.split_whitespace()
            .map(|n| n.parse().unwrap())
            .collect();
        let a = v[0]-1;
        let b = v[1]-1;
        graph.get_mut(a).unwrap().push(b);
        graph.get_mut(b).unwrap().push(a);
    }

    let res = graph[0].iter().find(|&x| graph[*x].iter().find(|&y| *y==n-1).is_some()).is_some();
    if res {
        println!("POSSIBLE")
    } else {
        println!("IMPOSSIBLE")
    }

}