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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Collections;
import java.util.List;
import java.util.Scanner;
import java.util.ArrayList;
import java.util.Stack;

public class Main {

	public static void main(String[] args) {
		Scanner stdin = new Scanner( System.in);
		int N,M;
		int a,b;
		List<Integer> alist=new ArrayList<Integer>() ;
		List<Integer> blist=new ArrayList<Integer>() ;
		N=stdin.nextInt();
		M=stdin.nextInt();
		for(int i=1;i<=M;i++){
			a=stdin.nextInt();
			b=stdin.nextInt();
			if(a==1)alist.add(b);
			if(b==N)blist.add(a);
		}
		Collections.sort(alist);
		Collections.sort(blist);
		Stack<Integer> astack=new Stack<Integer>();
		Stack<Integer> bstack=new Stack<Integer>();
		for(int i=0;i<alist.size();i++){
			astack.push(alist.get(i));
		}
		for(int i=0;i<blist.size();i++){
			bstack.push(blist.get(i));
		}
		
		if(astack.empty()||bstack.empty()){
			System.out.print("IMPOSSIBLE");
			System.exit(0);
		}
		a=astack.pop();
		b=bstack.pop();
		do{
			if(a<b){
				if(bstack.empty())break;
				b=bstack.pop();
			}
			if(a>b){
				if(astack.empty())break;
				a=astack.pop();
			}
			if(a==b){
				System.out.print("POSSIBLE");
				System.exit(0);
			}
		}while(true);
				
		System.out.print("IMPOSSIBLE");
	}
}