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-mcs 6.8.0.105) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using System.IO;
using static System.Console;

namespace atcorder2
{
    class Program
    {
        public static long Read()
        {
            return long.Parse(ReadLine());
        }

        public static long[] Reads()
        {
            return ReadLine().Split().Select(long.Parse).ToArray();
        }


        public static long gcd(long x,long y)
        {
            if (y < x) gcd(y, x);
            while (y != 0)
            {
                var z = x % y;
                x = y;
                y = z;
            }
            return x;
        }

        public static long C(long n,long k)
        {
            long x=1;
            for (long i = 1; i <=k; i++)
            {
                x *= n - i + 1;
                x /= i;
            }
            return x;
        }
        static void Main(string[] args)
        {
            var sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var q = Reads();
            var n = q[0];
            var m = q[1];
            var to = new bool[n];
            var from = new bool[n];
            for (int i = 0; i < m; i++)
            {
                q = Reads();
                if (q[0] == 1) to[q[1]-1] = true;
                if (q[1] == n) from[q[0]-1] = true;
            }
            var ans = false;
            for (int i = 0; i < n; i++)
            {
                if (to[i] && from[i]) ans = true;
            }
            WriteLine(ans ? "POSSIBLE" : "IMPOSSIBLE");

            Console.Out.Flush();
        }
    }
}