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: Runtime Error)

/*
     Author:Raghav Bansal
     IIIT Una
                  */
#include <bits/stdc++.h>
#define int long long int
#define pb push_back
#define mp make_pair
#define all(v) v.begin(),v.end()
#define BOLT ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL)
#define X first
#define Y second
#define endl "\n"
using namespace std;
void solve() {
    int n, m;
    cin >> n >> m;
    vector<array<int, 2>> ans;
    if (n & 1) {
        int a = 1, b = n / 2;
        while (a < b) {
            ans.pb({a, b});
            a++; b--;
        }
        a = n / 2 + 1, b = n - 1;
        while (a < b) {
            ans.pb({a, b});
            a++; b--;
        }
    } else {
        int a = 1, b = n;
        while (a < b) {
            ans.pb({a, b});
            a++; b--;
        }
    }
    for (int i = 0; i < m; i++) {
        cout << ans[i][0] << " " << ans[i][1] << endl;
    }
}
int32_t main() {
    BOLT;
    solve();
}