Problem: You are going to hold a competition of one-to-one game called AtCoder Janken. (Janken is the Japanese name for Rock-paper-scissors.) N players will participate in this competition, and they are given distinct integers from 1 through N. The arena has M playing fields for two players. You need to assign each playing field two distinct integers between 1 and N (inclusive). You cannot assign the same integer to multiple playing fields. The competition consists of N rounds, each of which proceeds as follows:

* For each player, if there is a playing field that is assigned the player's integer, the player goes to that field and fight the other player who comes there.
* Then, each player adds 1 to its integer. If it becomes N+1, change it to 1.



You want to ensure that no player fights the same opponent more than once during the N rounds. Print an assignment of integers to the playing fields satisfying this condition. It can be proved that such an assignment always exists under the constraints given.

Constraints

* 1 \leq M
* M \times 2 +1 \leq N \leq 200000

Input

Input is given from Standard Input in the following format:


N M


Output

Print M lines in the format below. The i-th line should contain the two integers a_i and b_i assigned to the i-th playing field.


a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print M lines in the format below. The i-th line should contain the two integers a_i and b_i assigned to the i-th playing field.


a_1 b_1
a_2 b_2
:
a_M b_M

Examples

Input

4 1


Output

2 3


Input

7 3


Output

1 6
2 5
3 4

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;
 


public class Main {
	private static Scanner sc = new Scanner(System.in);
	//result = Math.pow(num1, num3)
	//StringBuffer str = new StringBuffer(hoge1);
	//String hoge2 = str.reverse().toString();
	//map.containsKey(A)

	//Map<String, Integer> map = new HashMap<String, Integer>(n);
	/*for ( キーのデータ型 key : マップの名前.keySet() ) {
		データのデータ型 data = マップの名前.get( key );
		
		// keyやdataを使った処理;
	}*/
	//int i = Integer.parseInt(s);
	//Queue<String> qq=new ArrayDeque<>(); //add,poll,peek
	//Deque<String> qq=new ArrayDeque<>();//push,pop,peek
	//ArrayList<String> cc = new ArrayList<>(n);
	//Collections.sort(list);
	//Array.sort(list);   cc.contains(tmp)
	//Arrays.asList(c).contains("a")
	//list.set(1,"walk");//1 1 2 3 5
	//static long mod =1000000007;
	//static 	ArrayList<Integer> cc = new ArrayList<>(100);
	//for(int i=0;i<N;i++) {}
	static int a[]=new int[51];
	static int b[]=new int[51];
	static int c[]=new int[51];
	static int d[]=new int[51];
	
	
	
	
	public static void main(String[] args) {
		//String S=sc.next();
		
		//int N=sc.nextInt();for(int i=0;i<N;i++) {}
		int N=sc.nextInt();
		int M=sc.nextInt();
		
		int a=0,b=N+1;
	
		
		
		
		for(int i=M;i>0;i--) {
			if(i%2==0) {
				a++;
				p(a+" "+(a+i));
				
			}else {
				b--;
				p((b-i)+" "+b);	
			}
		}
		
		
		
	}
	
	
	/*int sum=0;
	 * for(int i=0;i<Q;i++) {
						if(t[b[i]-1]-t[a[i]-1]==c[i]) {
							sum+=d[i];
						}
					}
					ans=Math.max(ans, sum);
					*/
	
	
	
	
	

	


	
	static void p(String ans) {System.out.println(ans);};
	static void p(int ans) {System.out.println(ans);};
	static void p() {System.out.println();};
	static void p(long ans) {System.out.println(ans);};
	static void p(double ans) {System.out.println(ans);};
	static String nextPermutation(String s) {
		ArrayList<Character> list=new ArrayList<>();
		for(int i=0;i<s.length();i++) {
			list.add(s.charAt(i));
		}
		int pivotPos=-1;
		char pivot=0;
		for(int i=list.size()-2;i>=0;i--) {
			if(list.get(i)<list.get(i+1)) {
				pivotPos=i;
				pivot=list.get(i);
				break;
			}
		}
		if(pivotPos==-1&&pivot==0) {
			return "Final";
		}
		int L=pivotPos+1,R=list.size()-1;
		
		
		
		int minPos=-1;
		char min =Character.MAX_VALUE;
		
		for(int i=R;i>=L;i--) {
			if(pivot<list.get(i)) {
				if(list.get(i)<min) {
					min=list.get(i);
					minPos=i;
				}
			}
		}
		
		Collections.swap(list, pivotPos, minPos);
		Collections.sort(list.subList(L, R+1));
		
		
		StringBuilder sb=new StringBuilder();
		for(int i=0;i<list.size();i++) {
			sb.append(list.get(i));
		}
		return sb.toString();
	}
}