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::collections::HashMap;
use std::mem;

fn read_line() -> String{
    let mut s = String::new();
    io::stdin().read_line(&mut s).unwrap();
    s
}

fn read_ints() -> Vec<i32>{
    let s = read_line();
    let split:Vec<&str> = s.trim().split(" ").collect();
    split.iter().map(|&x| x.to_string().parse().unwrap()).collect()
}

fn main(){
    let temp = read_ints();
    let n = temp[0];
    let m = temp[1];
    
    let mut from1 = HashMap::new();
    let mut fromn = HashMap::new();
    
    for _i in 0..m{
        let temp = read_ints();
        let mut a = temp[0];
        let mut b = temp[1];
        
        if a>b{
            mem::swap(&mut a,&mut b);
        }
        
        if a == 1{
            
            match fromn.get(&b){
                Some(_) => {println!("POSSIBLE");return;},
                None    => {from1.insert(b,true);}
            }
        }
        
        if b == n{
            match from1.get(&a){
                Some(_) => {println!("POSSIBLE");return;},
                None    => {fromn.insert(a,true);}
            }
        }
    }
    println!("IMPOSSIBLE");
}