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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
use proconio::marker::Usize1;

fn adjacency_list(n: usize, ab: &Vec<(usize, usize)>) -> Vec<Vec<usize>> {
    let mut e = vec![vec![]; n];
    for &(a, b) in ab.iter() {
        e[a].push(b);
        e[b].push(a);
    }
    e
}

fn shortest_path(e: &Vec<Vec<usize>>, s: usize) -> Vec<usize> {
    let n = e.len();
    let inf = n;
    let mut d = vec![inf; n];
    let mut pq = std::collections::BinaryHeap::new();
    d[s] = 0;
    pq.push(std::cmp::Reverse((0, s)));
    while let Some(std::cmp::Reverse((c_u, u))) = pq.pop() {
        for &v in e[u].iter() {
            let c_v = c_u + 1;
            if c_v < d[v] {
                d[v] = c_v;
                pq.push(std::cmp::Reverse((c_v, v)));
            }
        }
    }
    d
}

fn main() {
    input! {
        n: usize,
        m: usize,
        ab: [(Usize1, Usize1); m],
    };
    let e = adjacency_list(n, &ab);
    let sp = shortest_path(&e, 0);
    let ans = if sp[n - 1] <= 2 {
        "POSSIBLE"
    } else {
        "IMPOSSIBLE"
    };
    println!("{}", ans);
}
*/

fn main() {
    let exe = "/tmp/bin441B13A3";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";