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: Time Limit Exceeded)

function Main(input) {
  	input = input.trim();
	var N = input.split("\n")[0].split(" ")[0];
  	var M = input.split("\n")[0].split(" ")[1];
  	var oneList = new Set();//1から行けるところのリスト
  	var NList = new Set();//Nから行けるところのリスト
  for(var i = 1; i <= M; i++){
    var tmp = input.split("\n")[i].split(" ").map((tmp)=>Number(tmp));
    if(tmp[0] == "1"){
       oneList.add(tmp[1]);
    }
    if(tmp[1] == N){
       NList.add(tmp[0]);
    }
  }
  if(oneList.length == 0 || NList.length == 0){
     console.log("IMPOSSIBLE");
  }else{
    for(i = 2; i < N; i++){
      if(oneList.has(i) && NList.has(i)){
         	console.log("POSSIBLE");
        return;
      }
    }
    console.log("IMPOSSIBLE");
  }
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));