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)

#[allow(unused_imports)]
use std::char::from_digit;
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::fs::File;
#[allow(unused_imports)]
use std::io::prelude::*;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufReader, BufWriter, Stdin, Stdout, Write};
#[allow(unused_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::str::FromStr;
 
type BoxResult<T> = Result<T, Box<std::error::Error>>;


fn main() {
    let mut scanner = Scanner::new(stdin());
    let line = scanner.read_vector::<usize>().unwrap();
    let (n, m) = (line[0], line[1]);
    let mut adj = vec![vec![]; n];
    for _ in 0..m {
        let line = scanner.read_vector::<usize>().unwrap();
        let (a, b) = (line[0] - 1, line[1] - 1);
        adj[a].push(b);
        adj[b].push(a);
    }

    if let Some(cost) = bfs(0, n - 1, &adj) {
        if cost == 2 {
            println!("POSSIBLE");
        } else {
            println!("IMPOSSIBLE");
        }
    } else {
        println!("IMPOSSIBLE");
    }
}

fn bfs(src: usize, snk: usize, adj: &[Vec<usize>]) -> Option<usize> {
    let mut queue = VecDeque::new();
    let mut used = vec![false; adj.len()];
    queue.push_front((src, 0));
    while queue.len() > 0 {
        let (crt, cost) = queue.pop_back().unwrap();
        if crt == snk {
            return Some(cost);
        }
        for &nxt in adj[crt].iter() {
            if used[nxt] {
                continue;
            }
            queue.push_front((nxt, cost + 1));
            used[nxt] = true;
        }
    }
    None
}

#[allow(dead_code)]
struct Scanner<R> {
    reader: BufReader<R>,
    buffer: String,
}
impl<R> Scanner<R>
where
    R: Read,
{
    #[allow(dead_code)]
    fn new(inner: R) -> Scanner<R> {
        let reader = BufReader::new(inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    #[allow(dead_code)]
    fn with_capacity(capacity: usize, inner: R) -> Scanner<R> {
        let reader = BufReader::with_capacity(capacity, inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
 
    #[allow(dead_code)]
    fn read_line(&mut self) -> BoxResult<String> {
        self.reader.read_line(&mut self.buffer)?;
        let cloned = self.buffer.trim().to_string();
        self.buffer.clear();
        Ok(cloned)
    }
 
    #[allow(dead_code)]
    fn read<T>(&mut self) -> BoxResult<T>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed = self.buffer.trim().parse()?;
        self.buffer.clear();
        Ok(parsed)
    }
    #[allow(dead_code)]
    fn read_vector<T>(&mut self) -> BoxResult<Vec<T>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed_vec = self
            .buffer
            .trim()
            .split_whitespace()
            .map(|s| s.parse())
            .collect::<Result<Vec<_>, _>>()?;
        self.buffer.clear();
        Ok(parsed_vec)
    }
    #[allow(dead_code)]
    fn read_matrix<T>(&mut self, lines: usize) -> BoxResult<Vec<Vec<T>>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        let mut parsed_matrix = vec![];
        for _ in 0..lines {
            self.reader.read_line(&mut self.buffer)?;
            parsed_matrix.push(
                self.buffer
                    .trim()
                    .split_whitespace()
                    .map(|s| s.parse())
                    .collect::<Result<Vec<_>, _>>()?,
            );
            self.buffer.clear();
        }
        Ok(parsed_matrix)
    }
    #[allow(dead_code)]
    fn read_chars(&mut self) -> BoxResult<Vec<char>> {
        self.reader.read_line(&mut self.buffer)?;
        let chars = self.buffer.trim().chars().collect::<Vec<_>>();
        self.buffer.clear();
        Ok(chars)
    }
}