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 Python (3.8.2) (judge verdict: Runtime Error)

def main():
    n, m = map(int, input().split())

    ans = [None for _ in range(m)]
    used = set()
    a = 1
    b = n
    good = True
    for i in range(m):
        if b - a == n - (b - a):
            a += 1
            b -= 1
        ans[i] = (a, b)
        if (b - a) in used:
            good = False
            break
        else:
            used.add(b - a)
        if (n - (b - a)) in used:
            good = False
            break
        else:
            used.add(n - (b - a))
        a += 1
        b -= 1

    if not good:
        ans = [None for _ in range(m)]
        used = set()
        a = 1
        b = n-1
        good = True
        for i in range(m):
            if b - a == n - (b - a):
                a += 1
                b -= 1
            ans[i] = (a, b)
            if (b - a) in used:
                good = False
                break
            else:
                used.add(b - a)
            if (n - (b - a)) in used:
                good = False
                break
            else:
                used.add(n - (b - a))
            a += 1
            b -= 1

    for i in range(m):
        print(ans[i][0], ans[i][1])

if __name__ == '__main__':
    main()