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