Problem:
Score : 500 points

Problem Statement

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

Sample Input 1

4 1

Sample Output 1

2 3

Let us call the four players A, B, C, and D, and assume that they are initially given the integers 1, 2, 3, and 4, respectively.

The 1-st round is fought by B and C, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 2, 3, 4, and 1, respectively.

The 2-nd round is fought by A and B, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 3, 4, 1, and 2, respectively.

The 3-rd round is fought by D and A, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 4, 1, 2, and 3, respectively.

The 4-th round is fought by C and D, who has the integers 2 and 3, respectively. After this round, A, B, C, and D have the integers 1, 2, 3, and 4, respectively.

No player fights the same opponent more than once during the four rounds, so this solution will be accepted.

Sample Input 2

7 3

Sample Output 2

1 6
2 5
3 4

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
#define FOR(i,l,r) for(long long i=(l);i<(r);++i)
#define REP(i,n) FOR(i,0,n)
#define REPS(i,n) FOR(i,0,n+1)
#define int long long
#define mp make_pair
#define pb push_back
#define eb emplace_back
const int MOD=1e9+7;
const int INF=1e18;

signed main(){
    int N,M;cin>>N>>M;
    int z;
    bool used[N+1];
  	REP(i,N+1)used[i]=false;
    if(N%2==1){
        z=M+1;
        for(int i=1;i<z;i++){
            cout<<i<<" "<<2*z-1-i<<endl;
        }
    }
    else{
        int M2=(N-1)/2;
        if(M2%2==0){
            int k=1;
            for(int i=M2;i>=1;i-=2){
                if(M==0)break;
                cout<<k<<" "<<k+i<<endl;
                k++;
                M--;
            }
            k= 2+M2;
            for(int i=M2-1;i>=1;i-=2){
                if(M==0)break;
                cout<<k<<" "<<k+i<<endl;
                k++;
                M--;
            }
        }
        if(M%2==1){
            int k=1;
            for(int i=M2;i>=1;i-=2){
                if(M==0)break;
                cout<<k<<" "<<k+i<<endl;
                k++;
                M--;
            }
            k= 2+M2;
            for(int i=M2-1;i>=1;i-=2){
                if(M==0)break;
                cout<<k<<" "<<k+i<<endl;
                k++;
                M--;
            }
        }
    }
}