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: Time Limit Exceeded)


use std::io::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
  let stdin = stdin();
  let stdin = stdin.lock();
  let token: String = stdin
    .bytes()
    .map(|c| c.expect("failed to read char") as char)
    .skip_while(|c| c.is_whitespace())
    .take_while(|c| !c.is_whitespace())
    .collect();
  token.parse().ok().expect("failed to parse token")
}

use std::cmp::{max, min};
use std::collections::HashMap;


fn main() {
  let n = read::<i64>();
  let m = read::<i64>();
  let mut map: HashMap<i64, Vec<i64>> = HashMap::new();

  for _ in 0..m {
    let a = read::<i64>();
    let b = read::<i64>();
    if map.contains_key(&a) {
      let current = map.get_mut(&a).unwrap();
      current.push(b)
    } else {
      map.insert(a, vec![b]);
    }

    if map.contains_key(&b) {
      let current = map.get_mut(&b).unwrap();
      current.push(a)
    } else {
      map.insert(b, vec![a]);
    }
  }

  let mut visited = vec![];
  let mut node = 1;
  let mut deep = 1;

  dfs(node, &mut visited, &map, deep);

  if visited.contains(&(n)) {
    println!("POSSIBLE");
  } else {
    println!("IMPOSSIBLE");
  }
}

fn dfs(node: i64, visited: &mut Vec<i64>, map: &HashMap<i64, Vec<i64>>, deep: i64) {
  // println!("node: {}", node);
  if 3 < deep {
    return;
  }
  if visited.contains(&node) {
    return;
  }
  visited.push(node);
  if map.contains_key(&node) {
    for (i, v) in map.get(&node).unwrap().iter().enumerate() {
      dfs(*v as i64, visited, map, deep + 1)
    }
  }

}