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)

#[macro_use]
mod input {

use std;
use std::io;

const SPLIT_DELIMITER: char = ' ';

#[macro_export]
#[allow(unused_macros)]
macro_rules! input {
    ( $($x:expr ),*) => {
        {
            let temp_str = input_line_str();
            let mut split_result_iter = temp_str.split_whitespace();
                $(
                let buf_split_result = split_result_iter.next();
                let buf_split_result = buf_split_result.unwrap();
                    ($x) = buf_split_result.parse().unwrap();
                )*
        }
    };
}

#[allow(dead_code)]
pub fn input_line_str() -> String {
    let mut s = String::new();
    io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

#[allow(dead_code)]
pub fn p<T>(t: T)
where
    T: std::fmt::Display,
{
    println!("{}", t);
}

#[allow(dead_code)]
pub fn input_vector2d<T>(line: usize) -> Vec<Vec<T>>
where
    T: std::str::FromStr,
{
    let mut v: Vec<Vec<T>> = Vec::new();

    for _ in 0..line {
        let vec_line = input_vector();
        v.push(vec_line);
    }
    v
}

#[allow(dead_code)]
pub fn input_vector<T>() -> Vec<T>
where
    T: std::str::FromStr,
{
    let mut v: Vec<T> = Vec::new();

    let s = input_line_str();
    let split_result = s.split(SPLIT_DELIMITER);
    for z in split_result {
        let buf = match z.parse() {
            Ok(r) => r,
            Err(_) => panic!("Parse Error"),
        };
        v.push(buf);
    }
    v
}

#[allow(dead_code)]
pub fn str2vec(s: &str) -> Vec<char> {
    let mut v: Vec<char> = Vec::new();
    for c in s.chars() {
        v.push(c);
    }
    v
}

}

use input::*;

fn dfs(g: &Vec<Vec<usize>>, from: usize, to: usize, remain: usize) -> bool {
    if remain == 0 {
        if to == from {
            return true;
        }
        return false;
    }

    for z in &g[from] {
        if dfs(g, *z, to, remain - 1) {
            return true;
        }
    }
    false
}

fn main() {
    let (n, m): (usize, usize);
    input!(n, m);
    let mut graph = vec![Vec::new(); n];
    for _ in 0..m {
        let (a, b): (usize, usize);
        input!(a, b);
        graph[a - 1].push(b - 1);
        graph[b - 1].push(a - 1);
    }

    if dfs(&graph, 0, n - 1, 2) {
        p("POSSIBLE");
    } else {
        p("IMPOSSIBLE");
    }
}