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 <iostream>
#include <iomanip>
#include <random>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <cmath>
#include <numeric>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <sstream>
#include <bitset>
#include <cassert>
#include <fstream>
#include <queue>

#define len(X) ((int)(X).size())

#ifdef __LOCAL
	#define DEBUG_OUTPUT_ENABLED 1
	#define DBG(X) dout << #X << "=" << (X) << '\n';
	#define SAY(X) dout << (X) << '\n';
#else
	#define DEBUG_OUTPUT_ENABLED 0
	#define DBG(X) 42;
	#define SAY(X) 42;
#endif

#define dout   ___debug::instance

using namespace std;
using ll = long long int;
using ull = unsigned long long int;
using ld  = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template<typename T, typename S> inline ostream& operator<<(ostream& os, const pair<T, S> p) { cout << "[" << p.first << ";" << p.second << "]"; return os; }
template<typename T> inline ostream& operator<<(ostream& os, const vector<T>& v) { for(auto el: v) cout << el << " "; return os; }
template<typename T> inline ostream& operator<<(ostream& os, const set<T>& v) { for(auto el: v) cout << el << " "; return os; }
template<typename T, typename S> inline ostream& operator<<(ostream& os, const map<T, S>& v) { for(auto el: v) cout << el << " "; return os; }
template<typename T> inline ostream& operator<<(ostream& os, const multiset<T>& v) { for(auto el: v) cout << el << " "; return os; }
namespace ___debug {
	struct DebugStream {
		private:
			bool is_first;
		public:
			DebugStream(bool _is_first): is_first(_is_first) {}
			template<typename T> DebugStream operator<<(const T& value) const {
				assert(DEBUG_OUTPUT_ENABLED);
				if(is_first) cout << "[DBG] ";
				cout << value;
				return DebugStream(false);
			};

			template<typename T> DebugStream printArray(T* l, T* r) {
				assert(DEBUG_OUTPUT_ENABLED);
				if(is_first) cout << "[DBG] ";
				while(l != r) {
					cout << (*l);
					++l;
					if(l == r) {
						cout << '\n';
					} else {
						cout << ' ';
					}
				}
				return DebugStream(false);
			}
	};
	DebugStream instance(true);
};

const int INT_INF = (int)(2e9);
const ll  LL_INF  = (ll)(2e18);

const int NIL = -1;
static mt19937 _g(time(nullptr));

inline ll randint(ll a, ll b) { ll w = (_g() << 31LL) ^ _g(); return a + w % (b - a + 1); }
inline void fast_io() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); };
template<typename T> inline T sign(T x) { return T(x > 0) - T(x < 0); }
template<typename T> inline T fetch() { T ret; cin >> ret; return ret; }
template<typename T> inline vector<T> fetch_vec(int sz) { vector<T> ret(sz); for(auto& elem: ret) cin >> elem; return ret; }

void solve() {
	int n = fetch<int>();
	int m = fetch<int>();
	for(int i = 0; i < m; ++i) {
		cout << 1 + i << ' ' << n - i << '\n';
	}
}

int main() {
	fast_io();
	solve();

	return 0;
}