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.split("\n");
  var n = parseInt(input[0].split(" ")[0]);
  var m = parseInt(input[0].split(" ")[1]);
  a= new Array(m).fill(0);
  b= new Array(m).fill(0);
  k= new Array();
  var ans = "IMPOSSIBLE";
  for(i=0;i<m;i++){
    tmp=input[i+1].split(" ");
    a[i]=tmp[0];
    b[i]=tmp[1];
    if(a[i]==1){
      k.push(b[i]);
    }
  }
  for(i=0;i<k.length;i++){
    if(ans=="POSSIBLE"){
      break;
    }
    for(j=0;j<m;j++){
      if(a[j]==k[i]){
        if(b[j]==n){
          ans="POSSIBLE";
          break;
        }
      }
    }
  }


  console.log('%s', ans);
}
  
// "実行する"ボタンを押した時に実行される関数 (デバッグ用)
function debug(){
  var input = document.getElementById("input").value;
  Main(input);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));