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: Accepted)

#include<bits/stdc++.h>
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define int long long
#define vec(a,n) vector<int> (a)((n));
#define Vec(a,n) vector<string> (a)((n));
#define twovec(a,n,m) vector<vector<int>> a(n,vector<int>(m,0));
#define Twovec(a,n,m) vector<vector<double>> a(n,vector<double>(m,0));
#define P pair<int,int>
#define All(a) (a).begin(),(a).end()
#define Sort(a) sort(All(a));
#define Reverse(a) reverse(All(a));
#define PQ(n) priority_queue<P,vector<P>,greater<P>> (n)
#define pq(n) priority_queue<int> (n)
#define print(a) cout << (a) << endl
#define printD(a) cout << setprecision(15) << (a) << endl;
using namespace std;
int max_int = 1000000007;
void Debug(auto a);
int nibul(auto a,auto b);
int nibuu(auto a,auto b);
void input(vector<auto>& a,int n);
double PI = 3.14159265358979;
int n;

signed main(){
    int m;
    cin >> n >> m;
    if(n%2==1){
        //平和
        REP(i,m){
            cout << m-i << " " << m+i+2 << endl;
        }
        return 0;
    }
    int t = n-2;
    int x = t/2;
    if(t%2==0){
        x--;
        x = x/2*2;
    }
    else{
        if(x%2==1) x++;
    }
    int l = min(m,(int)x/2+1);
    REP(i,l){
        cout << l-i << " " << l+i+1 << endl;
    }
    if(l==m) return 0;
    m -= l;
    l *= 2;
    int s = m;
    REP(i,s){
        cout << l+s-i << " " << l+s+i+2 << endl;
    }

    return 0;
}

void Debug(auto a){
    cout << "{ ";
    for(auto b: a){
        cout << b << " ";
    }
    cout << "}" << endl;
}

//key以上の初めてのitr
int nibul(auto a,auto b){return lower_bound(All(a),b) - a.begin();}
//key以下の最後のitr
int nibuu(auto a,auto b){return upper_bound(All(a),b) - a.begin()-1;}

void input(vector<auto>& a,int n){
    REP(i,n){
        cin >> a[i];
    }
}