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::*;

struct Scanner<R: BufRead> {
    handle: R,
    buffer: String,
    token: Vec<String>,
}

impl<R: BufRead> Scanner<R> {
    fn new(input: R) -> Self {
        Scanner {
            handle: input,
            buffer: String::new(),
            token: Vec::new(),
        }
    }
    fn next<T: FromStr>(&mut self) -> T {
        loop {
            if let Some(s) = self.token.pop() {
                match s.parse::<T>() {
                    Ok(v) => {
                        return v;
                    },
                    _ => panic!("Scanner error"),
                }
            }
            self.buffer.clear();
            self.handle.read_line(&mut self.buffer).ok();
            let mut i = 0;
            for s in self.buffer.split_whitespace().rev() {
                if i >= self.token.len() {
                    self.token.push(String::new());
                }
                self.token[i].clear();
                self.token[i].push_str(s);
                i += 1;
            }
        }
    }
}

fn main() {
    let stdin = std::io::stdin();
    let sc = &mut Scanner::new(stdin.lock());
    run(sc);
}

fn run(sc: &mut Scanner<StdinLock>) {
    let n: usize = sc.next();
    let m: usize = sc.next();
    let mut a = vec![(false, false); n + 1];
    for _ in 0..m {
        let x: usize = sc.next();
        let y: usize = sc.next();
        if x == 1 {
            a[y].1 = true;
        }
        if y == n {
            a[x].0 = true;
        }
    }
    if a.iter().any(|p| p.0 && p.1) {
        println!("POSSIBLE");
    } else {
        println!("IMPOSSIBLE");
    }
}