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)

#pragma GCC optimize("O3", "unroll-loops")
#pragma GCC target("sse4.2")

#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <bitset>
#include <sstream>
#include <deque>
#include <queue>
#include <complex>
#include <random>
#include <cassert>
#include <chrono>

using namespace std;

#define FAST ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define FIXED cout << fixed << setprecision(12)
#define ll long long
#define ld long double
#define pii pair<int, int>
#define pll pair<ll, ll>
#define graph vector<vector<int>>
#define pb push_back
#define pf push_front
#define popb pop_back
#define popf pop_front
#define f first
#define s second
#define hashmap unordered_map
#define hashset unordered_set
#define eps 1e-9
#define mod 1000000007
#define inf 3000000000000000007ll
#define sz(a) signed(a.size())
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()

#ifdef DEBUG
    mt19937 gen(857204);
#else
    mt19937 gen(chrono::high_resolution_clock::now().time_since_epoch().count());
#endif

#ifdef DEBUG
    template<class T> T to_dbg(T x) { return x; }
    template<class T, class U> string to_dbg(pair<T, U> p) {
        stringstream ss;
        ss << '{' << p.f << ',' << p.s << '}';
        return ss.str();
    }
    string to_dbg(string s) { return "\"" + s + "\""; }
    template<class T> string to_dbg(vector<T> a) {
        stringstream ss;
        ss << '{';
        if (sz(a)) ss << to_dbg(a[0]);
        for (int i = 1; i < sz(a); ++i)
            ss << "," << to_dbg(a[i]);
        ss << '}';
        return ss.str();
    }
    template<class T>
    void dbgout(T x) { cout << to_dbg(x) << endl; }
    template<class T, class... U>
    void dbgout(T t, U... u) {
        cout << to_dbg(t) << ", ";
        dbgout(u...);
    }
    #define dbg(...) cout << "[" << #__VA_ARGS__ << "] = ", dbgout(__VA_ARGS__);
#else
    #define dbg(...) 0
#endif

template<class T, class U> inline void checkmin(T &x, U y) { if (y < x) x = y; }
template<class T, class U> inline void checkmax(T &x, U y) { if (y > x) x = y; }
template<class T, class U> inline bool ifmax(T &x, U y) { if (y > x) return x = y, true; return false; }
template<class T, class U> inline bool ifmin(T &x, U y) { if (y < x) return x = y, true; return false; }
template<class T> inline void sort(T &a) { sort(all(a)); }
template<class T> inline void rsort(T &a) { sort(rall(a)); }
template<class T> inline void reverse(T &a) { reverse(all(a)); }
template<class T, class U> inline istream& operator>>(istream& str, pair<T, U> &p) { return str >> p.f >> p.s; }
template<class T> inline istream& operator>>(istream& str, vector<T> &a) { for (auto &i : a) str >> i; return str; }
template<class T> inline T sorted(T a) { sort(a); return a; }

signed main() {
    FAST; FIXED;
    int n, m;
    cin >> n >> m;
    vector<pii> p;
    if (n % 2 == 1) {
        for (int l = 1; l <= m; ++l) {
            p.pb({l, n - l + 1});
        }
    } else {
        for (int l = 1; l <= m; ++l)
            p.pb({l, n - l - 1});
        for (int i = 0; i < m && i < (n - 3) / 2; ++i)
            ++p[i].s;
    }
    for (auto i : p) cout << i.f << ' ' << i.s << '\n';
    #ifdef DEBUG
        cerr << "Runtime is: " << clock() * 1.0 / CLOCKS_PER_SEC << endl;
    #endif
    return 0;
}