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: Runtime Error)

#![allow(unused_imports)]
#![allow(clippy::many_single_char_names)]
#![allow(clippy::suspicious_arithmetic_impl)]

// using Rust(1.42.0)
// My Library Repo is at "https://github.com/Loptall/prcn_lib"
// check available crates on AtCoder at "https://atcoder.jp/contests/language-test-202001"

/*
    AtCoder Language Update 2020204 お疲れ様でした! 有難いです
*/

// Dep crates are...
use std::cmp::{max, min, Ordering};
use std::collections::{BTreeMap, BTreeSet, HashMap, HashSet, VecDeque};
use std::mem::swap;
use std::ops::*;
use std::{i128, i16, i32, i64, i8, isize, u128, u16, u32, u64, u8, usize};

use itertools::*;
use itertools_num::*;
use lazy_static::lazy_static;
use maplit::{btreemap, btreeset, hashmap, hashset};
use num_bigint::{BigInt, BigUint};
use num_integer::{binomial, gcd, lcm, Integer};
use permutohedron::Heap;
use proconio::{fastout, input, is_stdin_empty, marker::*};
use rand::random;

// code...
fn main() {
    input! {
        n: i64, m: i64,
    }

    if n % 2 == 1 {
        for dist in 1..=m {
            println!("{} {}", (n + dist) % n + 1, (n - dist) % n + 1);
        }
    } else {
        let mut left = n;
        let mut right = n + 1;
        for _i in 1..=m {
            println!("{} {}", left % n + 1 , right % n + 1);
            left -= 1;
            right += 1;
            if right - left == n / 2 {
                right += 1;
            }
            assert!(right % n + 1 < left % n + 1);
        }
    }
}