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.InputMismatchException;
import java.util.Arrays;

public class Main {
    static InputStream inStream;
    static PrintWriter out = new PrintWriter(System.out);
    static String INPUT = "";

    public static void main(String[] args) throws IOException {
        inStream = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        StringBuilder sb = new StringBuilder();
        int servs = nextInt();
        int cons = nextInt();
        int ap = nextInt();
        int cutS = 1;

        if(cons < servs-1 || cons >(servs-1)*(servs-2)/2+1) //check for viability
            out.println(-1);
        else{
            if(ap==1)
                cutS = 2;

            //connect isolated server to articulation point
            sb.append(cutS).append(" ").append(ap);
            out.println(sb);
            sb = new StringBuilder();

            //connect all other servers to articulation point
            for(int i=1; i<=servs; i++){
                if(i==cutS || i==ap)
                    continue;
                sb.append(i).append(" ").append(ap);
                out.println(sb);
                sb = new StringBuilder();
            }

            //connect other servers to each other while edges are left
            cons -= servs-1;
            //find next server that isn't ap or cut
            int nextAP = 1;

            while (cons > 0) {
                nextAP++;
                while(nextAP==cutS || nextAP==ap)
                    nextAP++;

                int j = nextAP+1;

                while (cons > 0 && j <= servs) {
                    if (j == ap) {
                        j++;
                        continue;
                    }
                    sb.append(j).append(" ").append(nextAP);
                    out.println(sb);
                    sb = new StringBuilder();
                    j++;
                    cons--;
                }
            }
        }

        out.flush();

    }


    private static boolean eof() {
        if (lenbuf == -1) return true;
        int lptr = ptrbuf;
        while (lptr < lenbuf) if (!isSpaceChar(inbuf[lptr++])) return false;
        try {
            inStream.mark(1000);
            while (true) {
                int b = inStream.read();
                if (b == -1) {
                    inStream.reset();
                    return true;
                } else if (!isSpaceChar(b)) {
                    inStream.reset();
                    return false;
                }
            }
        } catch (IOException e) {
            return true;
        }
    }

    private static byte[] inbuf = new byte[1024];
    static int lenbuf = 0, ptrbuf = 0;

    private static int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = inStream.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0)
                return -1;
        }
        return inbuf[ptrbuf++];
    }

    private static boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private static int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    private static double nextDouble() {
        return Double.parseDouble(nextString());
    }

    private static char nextChar() {
        return (char) skip();
    }

    private static String nextString() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private static StringBuilder nextStringBuilder() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb;
    }

    private static char[] nextString(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private static int[] nextArray0(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    private static int[] nextArray1(int n) {
        int[] a = new int[n + 1];
        for (int i = 1; i <= n; i++)
            a[i] = nextInt();
        return a;
    }

    private static long[] nextArrayLong1(int n) {
        long[] a = new long[n + 1];
        for (int i = 1; i <= n; i++)
            a[i] = nextLong();
        return a;
    }

    private static long[] nextArrayLong0(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    }

    private static int nextInt() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private static long nextLong() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
}