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;
typedef long long ll;
typedef pair<ll,ll> pl;
#define all(a) (a).begin(),(a).end()
#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(ll i = 0;i < (n);i++)
#define rep2(i,n) for(ll i = 0;i < (n);i++)
#define rep3(i,a,b) for(ll i = (a);i < (b);i++)
#define rep4(i,a,b,c) for(ll i = (a);i < (b);i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i = (n)-1;i >= 0;i--)
#define rrep2(i,n) for(ll i = (n)-1;i >= 0;i--)
#define rrep3(i,a,b) for(ll i = (a)-1;i >= (b);i--)
#define rrep4(i,a,b,c) for(ll i = (a)-1;i >= (b);i -= (c))
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define SHOW(x) cout << #x << ": " << x << endl;
template<class T> ll sumArr(const T& a){ return accumulate(all(a), 0LL);}
template<class T> auto minArr(const T& a){ return *min_element(all(a));}
template<class T> auto maxArr(const T& a){ return *max_element(all(a));}
template<class T> void DEBUG_PRINT(T tmp){cout<<tmp<<endl;}
template<class T1,class... T2> void DEBUG_PRINT(T1 tmp,T2... tmp2){cout<<tmp<<" ";DEBUG_PRINT(tmp2...);}
ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; }
const ll INF=1e18,MOD = 1e9+7;
const int iINF = 1e9;



int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    ll n,m;
    cin>>n>>m;
    ll mid = n/2,l = 1;
    if(n%2 == 1)l++;

    rrep(i,m)cout<<mid-i<<" "<<mid+l+i<<endl;

    return 0;
}