Problem: Bob got a job as a system administrator in X corporation. His first task was to connect n servers with the help of m two-way direct connection so that it becomes possible to transmit data from one server to any other server via these connections. Each direct connection has to link two different servers, each pair of servers should have at most one direct connection. Y corporation, a business rival of X corporation, made Bob an offer that he couldn't refuse: Bob was asked to connect the servers in such a way, that when server with index v fails, the transmission of data between some other two servers becomes impossible, i.e. the system stops being connected. Help Bob connect the servers.

Input

The first input line contains 3 space-separated integer numbers n, m, v (3 ≤ n ≤ 105, 0 ≤ m ≤ 105, 1 ≤ v ≤ n), n — amount of servers, m — amount of direct connections, v — index of the server that fails and leads to the failure of the whole system.

Output

If it is impossible to connect the servers in the required way, output -1. Otherwise output m lines with 2 numbers each — description of all the direct connections in the system. Each direct connection is described by two numbers — indexes of two servers, linked by this direct connection. The servers are numbered from 1. If the answer is not unique, output any.

Examples

Input

5 6 3


Output

1 2
2 3
3 4
4 5
1 3
3 5


Input

6 100 1


Output

-1

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class Code implements Runnable {

    public static void main(String[] args) throws IOException {
        new Thread(new Code()).start();
    }

    private void solve() throws IOException {
        int n = nextInt(), m = nextInt() - n + 1, v = nextInt() - 1;

        int choice = v == 0 ? v + 1 : v - 1;
        HashSet<Integer>[] net = new HashSet[n];
        for(int i = 0; i < n; ++i)  net[i] = new HashSet<Integer>();

        net[choice].add(v);
        net[v].add(choice);
        for(int i = 0; i < n; ++i) {
            if(i != v && i != choice) {
                net[v].add(i);
                net[i].add(v);
            }
        }

        for(int i = 0; i < n && m > 0; ++i) {
            if(i == v || i == choice)   continue;
            for(int j = 0; j < n && m > 0; ++j) {
                if(j == i || j == v || j == choice) continue;
                if(!net[j].contains(i)) {
                    net[j].add(i);
                    net[i].add(j);
                    m -= 1;
                }
            }
        }

        if(m != 0)  writer.println(-1);
        else {
            for(int i = 0; i < n; ++i) {
                for(int j : net[i]) {
                    writer.println((i + 1) + " " + (j + 1));
                    net[j].remove(i);
                }
            }
        }
    }

    private class Pair<E extends Comparable, V extends Comparable> implements Comparable<Pair<E, V>> {
        public Pair(E first, V second) {
            this.first = first;
            this.second = second;
        }

        @Override
        public int compareTo(Pair<E, V> obj) {
            if(first == obj.first)  return second.compareTo(obj.second);
            return first.compareTo(obj.first);
        }

        @Override
        public boolean equals(Object obj) {
            Pair other = (Pair)obj;
            return first.equals(other.first) && second.equals(other.second);
        }

        public E first;
        public V second;
    }

    @Override
    public void run() {
        try {
            if(in.equals(""))   reader = new BufferedReader(new InputStreamReader(System.in));
            else    reader = new BufferedReader(new FileReader(in));

            if(out.equals(""))  writer = new PrintWriter(new OutputStreamWriter(System.out));
            else    writer = new PrintWriter(new FileWriter(out));
            solve();
        } catch(IOException e) {
            e.printStackTrace();
        } finally {
            try {
                reader.close();
                writer.close();
            } catch(IOException e) {
                e.printStackTrace();
            }
        }
    }

    private int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    private long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    private double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    private float nextFloat() throws IOException {
        return Float.parseFloat(nextToken());
    }

    private String nextToken() throws IOException {
        while(st == null || !st.hasMoreTokens())    st = new StringTokenizer(reader.readLine());
        return st.nextToken();
    }

    private String in = "", out = "";
    private BufferedReader reader;
    private PrintWriter writer;
    private StringTokenizer st;
}