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::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn dfs(cn: usize, map: &Vec<Vec<usize>>, done: &mut Vec<bool>, tn: usize, d: usize) -> bool {
    if cn == tn {
        return true;
    }
    if done[cn] {
        return false;
    }
    if d >= 2 {
        return false;
    }
    done[cn] = true;
    for i in 0..map[cn].len() {
        let mi = map[cn][i];
        if !done[mi] {
            if dfs(mi, map, done, tn, d + 1) {
                return true;
            }
        }
    }
    return false;
}

fn main() {
    let n: usize = read();
    let m: usize = read();
    let mut map: Vec<Vec<usize>> = vec![vec![]; n + 1];

    for _ in 0..m {
        let a: usize = read();
        let b: usize = read();
        map[a].push(b);
        map[b].push(a);
    }
    let mut done: Vec<bool> = vec![false; n + 1];
    let result = dfs(1, &map, &mut done, n, 0);
    if result {
        println!("POSSIBLE");
    } else {
        println!("IMPOSSIBLE")
    }
}