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;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using static System.Console;
using static System.Math;
 
public class Hello{
    static public int mod = 1000000007;
    public static void Main(){
        // 方針
        // 
        int[] n = inta();
        var list1 = new List<int>();
        var listn = new List<int>();
        for(int i=0;i<n[1];i++){
            int[] temp = inta();
            if(temp[0] == 1){
                list1.Add(temp[1]);
            }
            if(temp[1] == n[0]){
                listn.Add(temp[0]);
            }
        }
        string ans = "IMPOSSIBLE";
        int[] map = new int[300000];
        
        foreach(var k in list1){
            map[k] = 1;
        }
        foreach(var k in listn){
            if(map[k] == 1){
                ans = "POSSIBLE";
                break;
            }
        }
        WriteLine(ans);
        
        
        
        
        
        
        
    }
    static int ncr(int n,int r){r = Min(r,n-r);long nn = 1;for(int i=n-r+1;i<=n;i++){nn = nn*i%mod;}long rr = 1;for(int i=1;i<=r;i++){rr = rr*i%mod;}rr = square((int)rr,mod-2);nn = nn * rr %mod;return (int)nn;}
    // a^b mod
    static int square(int a,int b){string binary = Convert.ToString(b,2);int bileng = binary.Length;long a_power = a;long value = 1;for(int i=bileng-1;i>=0;i--){if(binary[i] == '1'){value = value*a_power%mod;}a_power = a_power*a_power%mod;}return (int)value;}
    //static int square2(long a,long b,long m){var list = new List<int>();int temp = 1;long n2 = a;list.Add(1);int count = 1;while(temp < b){list.Add((int)n2);temp*=2;count++;n2 = n2*n2%m;}long ret = 1;while(b > 0){if(temp <= b){b -= temp;ret = ret*list[count]%1000000007;}count--;temp/=2;}return(int)ret;}
    //各種読取
    static string rstr(){ return ReadLine(); }
    static int rint(){ return int.Parse(ReadLine()); }
    static long rlong(){ return long.Parse(ReadLine()); }
    static string[] stra(){ return ReadLine().Split(' '); }
    static int[] inta(){ string[] read_str_array = ReadLine().Split(' '); int[] return_int_array = new int[read_str_array.Length]; for(int countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_int_array[countup_i] = int.Parse(read_str_array[countup_i]); } return return_int_array; }
    static int[,] inta2(int num_array,int in_array){ int[,] int_array2 = new int[num_array,in_array]; for(int i=0;i<num_array;i++){ int[] temp_array = inta(); for(int j=0;j<in_array;j++){ int_array2[i,j] = temp_array[j]; } } return int_array2; }
    static long[] longa(){ string[] read_str_array = ReadLine().Split(' '); long[] return_long_array = new long[read_str_array.Length]; for(long countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_long_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_long_array; }
    static double[] doublea(){ string[] read_str_array = ReadLine().Split(' '); double[] return_double_array = new double[read_str_array.Length]; for(long countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_double_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_double_array; }
    // -----------------------------
    static long divideup(long divided,long divid){ long temp_divide = divided/divid; if(divided % divid > 0){ temp_divide++; } return temp_divide; }
    static long GCD(long a,long b){ if(a < b){ long temp = a; a = b; b = temp; } if(a % b == 0){ return b; } else{ long temp = b; b = a%b; a = temp; return GCD(a,b); } }
    static long LCM(long a,long b){ return a * b / GCD(a,b); }
}



//知見
// (string) hogestr -> (char[]) hoge
    // char hoge = hogestr.ToCharArray();
// (char[]) hoge -> (string) hogestr
    // string hoge = new string(hoge);
// Hashtable ×  Dictionary ○
// Dictionary hoge<string,int>
    // hoge.ContainsKey(string) -> return boolean
    // hoge[string] -> return int
    // hoge[int] -> CE
// Dictionary hoge<int1,int2>
    // hoge<int1,int2>: hoge[int1] -> return int2
    // KeyValuePair<int,int> k <-> k.Key == int1 / k.Value == int2
// SortedDictionary() > SortedList() ???
// キュー　-> 幅優先 ???
    // var queue = new Queue<int>(); queue.Enqueue() queue.Dequeue()
// スタック -> 深さ優先 ???
    // var stack = new Stack<int>(); stack.Push(hoge) stack.Pop() stackPeek() stack.Count
// if (list?.Count > 0) リストが空でもnullでもない
// ソート
    // list.Sort(StringComparer.Ordinal); listの(辞書順?)ソート
        // StringComparer.Ordinal とは
// 出力
    // foreach(var a int list){ WriteLine(a); } より
        // WriteLine(string.Join("\n", list)); が速い
    //var sw = new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false};
    //    Console.SetOut(sw);
    //    foreach(var k in list[num-1]){
    //        WriteLine(k);
    //    }
    //    Console.Out.Flush();