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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

"use strict";
    
const main = arg => {
    arg = arg.trim().split("\n");
    const N = parseInt(arg[0].split(" ")[0]);
    const M = parseInt(arg[0].split(" ")[1]);
    
    const ab = arg.slice(1, M + 1);
    
    let map = [...Array(N)].fill(0);
    let answer = "IMPOSSIBLE";
    
    for(let i=0; i<M; i++) {
        let temp = ab[i].split(" ").map(n=>parseInt(n));
        let from = temp[0];
        let to   = temp[1];
        
        if(from === 1) {
            if(map[to] === N) {
                answer = "POSSIBLE";
                break;
            } else {
                map[to]++;
            }
        }
        
        if(to === N) {
            if(map[from] === 1) {
                answer = "POSSIBLE";
                break;
            } else {
                map[from]++;
            }
        }
    }
        
    console.log(answer);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));