Let's call an undirected graph of n vertices p-interesting, if the following conditions fulfill: 

  * the graph contains exactly 2n + p edges; 
  * the graph doesn't contain self-loops and multiple edges; 
  * for any integer k (1 ≤ k ≤ n), any subgraph consisting of k vertices contains at most 2k + p edges. 



A subgraph of a graph is some set of the graph vertices and some set of the graph edges. At that, the set of edges must meet the condition: both ends of each edge from the set must belong to the chosen set of vertices. 

Your task is to find a p-interesting graph consisting of n vertices.

Input

The first line contains a single integer t (1 ≤ t ≤ 5) — the number of tests in the input. Next t lines each contains two space-separated integers: n, p (5 ≤ n ≤ 24; p ≥ 0; <image>) — the number of vertices in the graph and the interest value for the appropriate test. 

It is guaranteed that the required graph exists.

Output

For each of the t tests print 2n + p lines containing the description of the edges of a p-interesting graph: the i-th line must contain two space-separated integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi) — two vertices, connected by an edge in the resulting graph. Consider the graph vertices numbered with integers from 1 to n. 

Print the answers to the tests in the order the tests occur in the input. If there are multiple solutions, you can print any of them.

Examples

Input

1
6 0


Output

1 2
1 3
1 4
1 5
1 6
2 3
2 4
2 5
2 6
3 4
3 5
3 6
import java.util.*;
import java.math.*;
import java.io.*; 
 public class A{

static FastReader scan=new FastReader();
  public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
  static LinkedList<Long>edges[];
  static LinkedList<Integer>Same[];
  static LinkedList<Integer>Dif[];
  static LinkedList<Integer>integers[];
static int []dx={1,-1,0,0};
static int []dy={0,0,1,-1};
static boolean prime[];
static long LCM(long a,long b){
    return (Math.abs(a*b))/gcd(a,b);
   }
   static long gcd(long a, long b) {
    if(a!=0&&b!=0)
        while((a%=b)!=0&&(b%=a)!=0);
    return a^b;
}
static int countSetBits(int n) 
    { 
        int count = 0; 
        while (n > 0) { 
            count += n & 1; 
            n >>= 1; 
        } 
        return count; 
    } 
 static void sieve(int n) 
    { 
        
        prime = new boolean[n+1]; 
        for(int i=0;i<n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p*p <=n; p++) 
        { 
           
            if(prime[p] == true) 
            { 
                
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 
    }  
    static int[] arr,ans;
    static int count;
 
  static boolean canTransmit[][]=new boolean[1000+5][1000+5];

    
    
    static boolean vis[][];
    static int color[]=new int[(int)1e5+5];
   static long cnt[]=new long[2];
static boolean bad=false;
    static void dfs(int v,int col){
        
        color[v]=col;
        for(int i:Dif[v])
        {
            if(~color[i]!=0)
            {
                if(color[i]==color[v])
                    bad=true;
                
            }
            else dfs(i,col^1);
        }
 for(int i:Same[v])
        {
            if(~color[i]!=0)
            {
                if(color[i]==(color[v]^1))
                    bad=true;
                
            }
            else dfs(i,col);
        }
            }
            static char grid[][];
            static char copy[][];
            static int N;
            static boolean e(int x,int y){
                return(x>=0&&x<N&&y>=0&&y<N);
            }
           static void dfs(int x,int y,int w){
              if(x < 0 || y < 0 || x >= N || y >= N)
        return ;
            if(vis[x][y]||grid[x][y]!=w)
                return;
            vis[x][y]=true;

            dfs(x+1,y,w);
            dfs(x-1,y,w);
            dfs(x,y+1,w);
            dfs(x,y-1,w);

           }

public static void main(String[] args)  throws IOException 
{
//java.util.Scanner scan=new java.util.Scanner(new File("revegetate.in"));
 //PrintWriter out = new PrintWriter (new FileWriter("revegetate.out"));
  //  System.out.println(~-1);
    

        //System.out.println(0^1);
 int t=scan.nextInt();
 while(t-->0)
 {
    int cnt=0;
    int n=scan.nextInt();
    int p=scan.nextInt();
    outer:for(int i=1;i<=n&&cnt<2*n+p;i++)
    {
        for(int j=i+1;j<=n;j++)
        {
            if(cnt==2*n+p)
               break outer;
           else {
            System.out.println(i+" "+j);
            cnt++;


           }
        }
    }

 }
out.close();


}
static double dis(double x1,double y1,double x2,double y2)
{
    return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}
static int mod(int x,int y)
    {
        if(x<0)
            x=x+(-x/y+1)*y;
        return x%y;
    }
 public static  long pow(long b, long e) {
            long r = 1;
            while (e > 0) {
                if (e % 2 == 1) r = r * b ;
                b = b * b;
                e >>= 1;
            }
            return r;
        }
private static void sort(long[] arr) {
        List<Long> list = new ArrayList<>();
        for (long object : arr) list.add(object);
        Collections.sort(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }
 public static class FastReader {
        BufferedReader br;
        StringTokenizer root;
        
 
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        boolean hasNext(){
            String line;
            while(root.hasMoreTokens())
                return true;
            return false;
        }
 
        String next() {
            while (root == null || !root.hasMoreTokens()) {
                try {
                    root = new StringTokenizer(br.readLine());
                } catch (Exception addd) {
                    addd.printStackTrace();
                }
            }
            return root.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
 
        long nextLong() {
            return Long.parseLong(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (Exception addd) {
                addd.printStackTrace();
            }
            return str;
        }
         public int[] nextIntArray(int arraySize) {
            int array[] = new int[arraySize];
 
            for (int i = 0; i < arraySize; i++) {
                array[i] = nextInt();
            }
 
            return array;
        }
}
 static class Pair implements Comparable<Pair>{
        public int x, y;
        public Pair(int x1, int y1) {
            x=x1;
            y=y1;
        }
        @Override
        public int hashCode() {
            return (int)(x + 31 * y);
        }
        public String toString() {
            return x + " " + y;
        }
        @Override
        public boolean equals(Object o){
            if (o == this) return true;
            if (o.getClass() != getClass()) return false;
            Pair t = (Pair)o;
            return t.x == x && t.y == y;
        }
public int compareTo(Pair o)
{
    return (x-o.y)-(o.x-y);

    }

static class pair{
    int i;
    int j;
pair(int i,int j){
    this.i=i;
    this.j=j;
}}}
 static class tuple{
        int x,y,z;
        tuple(int a,int b,int c){
            x=a;
            y=b;
            z=c;
        }
    }
    static class Edge{
        int d,w;
        Edge(int d,int w)
        {
            this.d=d;
            this.w=w;
        }
    }
}









