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 Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused)]

fn solve<R: std::io::BufRead>(mut sc: Scanner<R>) {
    let n: usize = sc.get();
    let m: usize = sc.get();

    let mut ds: Vec<usize> =
        (1..=m).map(|d| if d % 2 != 0 { d } else { n - d }).collect();

    for d in 1..=m {
        if d % 2 != 0 {
            let a = n / 2 - d / 2;
            println!("{} {}", a, a + ds[d - 1]);
        } else {
            let a = d / 2;
            println!("{} {}", a, a + ds[d - 1]);
        }
    }
}

macro_rules! debug {
    ($($a:expr),*) => {
        eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

//
// Based on EbTech's Scanner https://stackoverflow.com/q/56449027
//
struct Scanner<'a, R: std::io::BufRead> {
    reader: R,
    buf: String,
    iter: std::str::SplitWhitespace<'a>,
}

impl<'a, R: std::io::BufRead> Scanner<'a, R> {
    fn new(reader: R) -> Self {
        Self { reader, buf: String::new(), iter: "".split_whitespace() }
    }

    fn get<T: std::str::FromStr>(&mut self) -> T {
        if let Some(t) = self.iter.next() {
            return t.parse().ok().expect("Parse error")
        }
        self.buf.clear();
        self.reader.read_line(&mut self.buf).expect("I/O error");
        self.iter = unsafe { std::mem::transmute(self.buf.split_whitespace()) };
        self.get()
    }

    fn gets<T: std::iter::FromIterator<char>>(&mut self) -> T {
        use std::io::Read;
        assert_eq!(self.iter.next(), None);
        self.reader
            .by_ref()
            .bytes()
            .map(|b| b.unwrap() as char)
            .skip_while(|&c| c.is_whitespace())
            .take_while(|&c| !c.is_whitespace())
            .collect()
    }
}

fn main() {
    let stdin = std::io::stdin();
    solve(Scanner::new(stdin.lock()));
}