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 test4 {
	static int n;
	static Queue<pair>a;
	 public static void main(String[] args) throws IOException, InterruptedException {
			Scanner sc=new Scanner(System.in); 
			int n=sc.nextInt();
			int m=sc.nextInt();
			int v=sc.nextInt()-1;
			int m1=m;
	        a=new LinkedList();
			boolean f=true; int j;
			int []b=new int [n-1]; int y=0;
			for( j=0;j<n;j++) {
				if(j!=v) {
					a.add(new pair(v+1,j+1)); b[y]=j; y++;
				   m1--;
				   }
			}
		outer:	
            for(int i=0;i<n-1;i++) {
            	if(i==n-2) {
            		f=false;
                    break  outer;        	
            	}
            	if(m1<=0) {
            		break;
                   }
            	for(int u=i+1;u<n-2;u++) {
            		 a.add(new pair(b[i]+1,b[u]+1));
            		 m1--;
            		if(m1==0)
            			break outer;
            	}
            }
			if(n-m>1)
				f=false;
			if(!f)
				System.out.println(-1);
			else {
				for(int o=0;o<m;o++) {
					System.out.println(a.remove());
				}
			}
	 }
	 static boolean check(int x,int y) {
		 if(a.contains(new pair(x,y)))
		   return true;
		 if(a.contains(new pair(y,x)))
			 return true;
		 return false;
	 }
	 static class pair{
		 int from;
		 int to; 
		 public String toString() {
			 return from+" "+to; 
		 }
		 pair(int f,int t){
			 from=f;
			 to=t;
		 }
	 }
	static	class Scanner{ 
        StringTokenizer st;
        BufferedReader br;
        public Scanner(InputStream system) {br = new BufferedReader(new InputStreamReader(system));}
        public Scanner(String file) throws Exception {br = new BufferedReader(new FileReader(file));}
        public String next() throws IOException
        {
            while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
        public String nextLine()throws IOException{return br.readLine();}
        public int nextInt() throws IOException {return Integer.parseInt(next());}
        public double nextDouble() throws IOException {return Double.parseDouble(next());}
        public char nextChar()throws IOException{return next().charAt(0);}
        public Long nextLong()throws IOException{return Long.parseLong(next());}
        public boolean ready() throws IOException{return br.ready();}
        public void waitForInput() throws InterruptedException {Thread.sleep(3000);}
    }
}