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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using static System.Math;
using static System.Console;
using static CS_Contest.Utils;

namespace CS_Contest {
	using Li = List<int>;
	using LLi = List<List<int>>;
    class Program {
        static void Main(string[] args) {
			new Calc().Solve();
			return;
        }

		private class Calc {
			Li NM;
			Tree g;
			public void Solve() {
				NM = ReadInt(' ');
				g = new Tree(NM[0]);
				string IMP = "IMPOSSIBLE", POS = "POSSIBLE";
				REP(NM[1], x => {
					var ab = ReadInt(' ').Select(y=>y-1).ToList();
					g.Add(ab[0], ab[1]);
				});
				if (dfs(0, 0)) POS.WL();
				else IMP.WL();
				return;
			}
			bool dfs(int from,int step) {
				if (step > 2) return false;
				if (step == 2) return from == NM[0] - 1;
				return g.Graph[from].Any(x => dfs(x, step + 1));
			}
		}
    }

	
	
    public static class Utils {
        public static void WL(this object obj) => WriteLine(obj);
        public static void WL(this string obj) => WriteLine(obj);
        public static void WL<T>(this IEnumerable<T> list) => list.ToList().ForEach(x => x.WL());
		public static int ReadInt() => int.Parse(ReadLine());
		public static List<int> ReadInt(char s) => ReadLine().Split(s).Select(int.Parse).ToList();
		public static long ReadLong() => long.Parse(ReadLine());
		public static List<long> ReadLong(char s) => ReadLine().Split(s).Select(long.Parse).ToList();
		public static void REP(int n,Action<int> act) {
			for (int i = 0; i < n; i++) {
				act(i);
			}
		}
		public static void RREP(int n,Action<int> act) {
			for (int i = n-1; i >=0; i--) {
				act(i);
			}
		}
		public static void Yes() => "Yes".WL();
		public static void No() => "No".WL();

		public class Tree {
			public LLi Graph;
			public Tree(int nodes) {
				Graph = new LLi();
				REP(nodes, x => {
					Graph.Add(new Li());
				});
			}
			public void Add(int x,int y) {
				Graph[x].Add(y);
				Graph[y].Add(x);
			}
		}
    }
}