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)


mod scanner {
    use std::io::StdinLock;
    use std::str::FromStr;
    use std::io::BufRead;
    pub struct Scanner<'a> {
        stdin: StdinLock<'a>,
        token: Vec<String>,
    }
    impl<'a> Scanner<'a> {
        pub fn new(stdin: StdinLock) -> Scanner {
            Scanner {
                stdin: stdin,
                token: vec![],
            }
        }
        pub fn read<T: FromStr>(&mut self) -> T {
            loop {
                if let Some(token) = self.token.pop() {
                    return token.parse().ok().unwrap();
                }
                let mut s = String::new();
                self.stdin.read_line(&mut s).unwrap();
                self.token = s.trim().split_whitespace().rev().map(String::from).collect();
            }
        }
    }
}

fn main() {
    run();
}

fn run() {
    let stdin = std::io::stdin();
    let mut sc = scanner::Scanner::new(stdin.lock());
    let n: usize = sc.read();
    let m: usize = sc.read();
    let mut x = vec![false; n + 1];
    let mut y = vec![false; n + 1];
    for _ in 0..m {
        let a: usize = sc.read();
        let b: usize = sc.read();
        if a == 1 {
            x[b] = true;
        }
        if b == n {
            y[a] = true;
        }
    }
    if x.iter().zip(y.iter()).any(|(a, b)| *a && *b) {
        println!("POSSIBLE");
    } else {
        println!("IMPOSSIBLE");
    }
}