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)

// TLE?
#include<iostream>
#include<vector>
using namespace std;

int main(){
    int n, m;
    cin >> n >> m;
    vector<int> a(m), b(m);
    vector<bool> ng(n+1, 0), used(n+1, 0);
    for(int i = 1; i <= m; i++) a[i-1] = i, used[i] = true;
    for(int i = 1; i <= m; i++) b[i-1] = m+m-i+1, used[m+m-i+1] = true;
    for(int i = 0; i < m; i++){
        int val = abs(b[i]-a[i]);
        if(ng[val] || ng[n-val]){
            for(int to = n; to >= 1; to--){
                if(used[to])    continue;
                int nval = abs(to-a[i]);
                if(ng[nval] || ng[n-nval])  continue;
                used[b[i]] = false;
                used[to] = true;
                b[i] = to;
                break;
            }
        }else{
            ng[val] = ng[n-val] = true;
        }
    }
    for(int i = 0; i < m; i++)  cout << a[i] << " " << b[i] << endl;
    return 0;
}