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)

// inputに入力データ全体が入る
function Main(input) {
    // 1行目がinput[0], 2行目がinput[1], …に入る
   	input = input.split("\n");
  	var tmp = input[0].split(" ");
    //文字列から10進数に変換するときはparseIntを使います
    var goalIsland = parseInt(tmp[0], 10);
    var shipVariation = parseInt(tmp[1], 10);
    var shipVariationArray = new Array(shipVariation);
  	var successCheck =0;
  	for(var i=0; i<shipVariation; i++){
    	shipVariationArray[i] = input[i+1].split(" ");
    }
  	for(var fromI=0; fromI<shipVariation; fromI++){
      if(parseInt(shipVariationArray[fromI][0])==1){
     	for(var fromJ=0; fromJ<shipVariation; fromJ++){
       		if(parseInt(shipVariationArray[fromJ][0])==parseInt(shipVariationArray[fromI][1])){
              if(parseInt(shipVariationArray[fromJ][1])==goalIsland){
                successCheck=1;
                break;
              }
            }
        }
        
      }
    }
    //出力
  	if(successCheck==1){
		console.log('POSSIBLE');
    }
  	else{
   		console.log('IMPOSSIBLE'); 
    }
}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));