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.io.*;
    import java.util.*;

    public class Main {

        public static void main(String[] args) throws IOException {

            boolean local = false;
            if (args.length > 0 && args[0].equals("LOCAL"))
                local = true;

            new Main(local).go();
        }

        boolean LOCAL;
        PrintWriter out;
        Reader in;
        BufferedReader br;

        Main(boolean local) throws IOException {

            this.LOCAL = local;

            try {

                //br = new BufferedReader( new FileReader("input.txt") );
                in = new Reader("input.txt");
                out = new PrintWriter( new BufferedWriter(new FileWriter("output.txt")) );
            }
            catch (Exception e) {

                //br = new BufferedReader( new InputStreamReader( System.in ) );
                in = new Reader();
                out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );
            }
        }

        void go() throws IOException {

            int t = 1;

            if (this.LOCAL)
                t = in.nextInt();

            while (t > 0) {

                solve();
                t--;

                if (LOCAL)
                    out.println();

            }

            out.flush();
            out.close();
        }


        int inf = 2000000000;
        int mod = 1000000007;
        double eps = 1e-9;

        int n;
        int m;

        ArrayList<Integer>[] g = new ArrayList[200010];

        void solve() throws IOException {

            int n = in.nextInt();
            int m = in.nextInt();

            for (int i = 0; i < n; i++)
                g[i] = new ArrayList<>();

            for (int i = 0; i < m; i++) {

                int x = in.nextInt()-1;
                int y = in.nextInt()-1;

                if (x == n-1 && y == 0 || x == 0 && y == n-1)
                    continue;

                g[x].add(y);
                g[y].add(x);
            }

            Queue<Integer> q = new LinkedList<>();
            q.add(0);
            int[] d = new int[n];
            Arrays.fill(d, inf);
            d[0] = 0;

            while (!q.isEmpty()) {

                int v = q.poll();
                for (int u : g[v])
                    if (d[v]+1 < d[u]) {
                        d[u] = d[v] + 1;
                        q.add(u);
                    }
            }

            if (d[n-1] == 2)
                out.println("POSSIBLE");
            else
                out.println("IMPOSSIBLE");

        }


        class Edge implements Comparable<Edge> {

            int a;
            int b;
            int c;
            int i;

            Edge(int a, int b, int c, int i) {

                this.a = a;
                this.b = b;
                this.c = c;
                this.i = i;
            }

            public int compareTo(Edge p) {

                if (c > p.c) return 1;
                if (c < p.c) return -1;
                if (i > p.i) return 1;
                if (i < p.i) return -1;
                return 0;
            }
        }

        class Pair implements Comparable<Pair>{

            int a;
            int b;

            Pair(int a, int b) {

                this.a = a;
                this.b = b;
            }

            public int compareTo(Pair p) {

    //            if (a > p.a) return 1;
    //            if (a < p.a) return -1;
                if (b > p.b) return 1;
                if (b < p.b) return -1;
                return 0;
            }
        }

        class Item {

            int a;
            int b;
            int c;

            Item(int a, int b, int c) {
                this.a = a;
                this.b = b;
                this.c = c;
            }

        }

        class Reader {

            BufferedReader  br;
            StringTokenizer tok;

            Reader(String file) throws IOException {
                br = new BufferedReader( new FileReader(file) );
            }

            Reader() throws IOException {
                br = new BufferedReader( new InputStreamReader(System.in) );
            }

            String next() throws IOException {

                while (tok == null || !tok.hasMoreElements())
                    tok = new StringTokenizer(br.readLine());
                return tok.nextToken();
            }

            int nextInt() throws NumberFormatException, IOException {
                return Integer.valueOf(next());
            }

            long nextLong() throws NumberFormatException, IOException {
                return Long.valueOf(next());
            }

            double nextDouble() throws NumberFormatException, IOException {
                return Double.valueOf(next());
            }


            String nextLine() throws IOException {
                return br.readLine();
            }

        }

    }