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 Ruby (2.7.1) (judge verdict: Accepted)

# https://atcoder.jp/contests/abc165/tasks/abc165_e

N, M = gets.split.map(&:to_i)

# - Nが奇数の場合
#   1, 3, ... , 2*M+1 の距離となるペアを生成
#   反対側から数えた距離との組み合わせは常に奇数+偶数になるので、
#   全て混ぜても重複しない
# - Nが偶数の場合
#   1, 3, ... , N/2-2, N/2+1, ... , 2*M
#   または
#   1, 3, ... , N/2-1, N/2+2, ... , 2*M
#   の距離となるペアを生成
#   距離が奇数+奇数または偶数+偶数の組み合わせで生成されるので
#   同じ奇数+奇数が発生する前に片方の位置を1ずらして偶数+偶数に変える

a = N / 2
b = N / 2 + 1
M.times do
  puts "#{a} #{b}"
  a -= 1
  b += 1
  d = b - a
  a -= 1 if N.even? && d.odd? && d >= N - d
end