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::str::FromStr;

fn get_one<T : FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    return s.trim().parse().ok().unwrap();
}

fn get_vec<T : FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    return s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect();
}

fn bfs(edges : Vec<Vec<usize>>, stt : usize) -> Vec<i32> {
    let mut v : Vec<i32> = vec!(-1;edges.len());
    let mut que = std::collections::VecDeque::new();
    que.push_back(stt);
    v[stt] = 0;
    while !que.is_empty() {
        let x : usize = que.pop_front().unwrap();
        for next in edges[x].iter() {
            if v[*next] == -1 {
                v[*next] = v[x] + 1;
                que.push_back(*next);
            }
        }
    }
    return v;
}

fn main() {
    let nm : Vec<usize> = get_vec();
    let n = nm[0];
    let m = nm[1];

    let mut edges : Vec<Vec<usize>> = vec!(Vec::new();n);
    for _i in 0..m {
        let ab : Vec<usize> = get_vec();
        edges[ab[0]-1].push(ab[1]-1);
        edges[ab[1]-1].push(ab[0]-1);
    }
    let ans : Vec<i32> = bfs(edges, 0);
    println!("{}", if ans[n-1] != -1 && ans[n-1] <= 2 {"POSSIBLE"} else {"IMPOSSIBLE"});
}