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: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.ComponentModel;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using static System.Console;
using static System.Math;
class Simple
{
    int N, M;
    int[] a, b;
    void Solve() {
        //input
        N = io.Int;
        M = io.Int;
        a = new int[M];
        b = new int[M];
        for (int i = 0; i < M; ++i) {
            a[i] = io.Int;
            b[i] = io.Int;
        }
        //cal
        var ziped = a.Zip(b, (v1, v2) => new { v1, v2 });
        var from1 = ziped.Where(v => v.v1 == 1).Select(v => v.v2);
        var toN   = ziped.Where(v => v.v2 == N).Select(v => v.v1);
        var ans   = from1.Any(v => toN.Contains(v));
        //ret
        WriteLine(ans ? "POSSIBLE" : "IMPOSSIBLE");
    }
    SimpleIO io = new SimpleIO();
    public static void Main(string[] args) => new Simple().Stream();
    private void Stream() {
        //var exStdIn = new System.IO.StreamReader("stdin.txt");
        //SetIn(exStdIn);
        Solve();
        io.Flush();
    }
}
class SimpleIO
{
    string[] _nextBuffer;
    int _bufferCnt;
    char[] cs = new char[] { ' ', '"', ',' };
    StreamWriter sw = new StreamWriter(OpenStandardOutput()) {
        AutoFlush = false
    };
    public SimpleIO() {
        _nextBuffer = new string[0];
        _bufferCnt = 0;
        SetOut(sw);
    }
    string Next() {
        if (_bufferCnt < _nextBuffer.Length)
            return _nextBuffer[_bufferCnt++];
        var st = ReadLine();
        while (st == "")
            st = ReadLine();
        if (st != null)
            _nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        else
            st = "";
        _bufferCnt = 0;
        return _nextBuffer[_bufferCnt++];
    }
    public string String => Next();
    public char Char => char.Parse(String);
    public int Int => int.Parse(String);
    public long Long => long.Parse(String);
    public double Double => double.Parse(String);
    public void Flush() => Out.Flush();
}