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 (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):   
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd 
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrsruvwxyz')
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    
        
        
            
            
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    
    
    N, M = R()
    if N%2 == 0: 
        j = 2
        for i in range(1, M+1):
            if j == (N+6)//4:
                j+=1
            print(j, N+1-i)
            j += 1
    else: 
        for i in range(M):
            print(i+2, N-i)

    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Solution (Python):

import sys


def check(N, M, ans):
    p = list(range(1, N+1))
    s = set()
    for _ in range(N):
        for a, b in ans:
            s.add((min(p.index(a), p.index(b)), max(p.index(a), p.index(b))))
        p = [p[-1]] + p[:-1]
    assert len(s) == N * M


def solve(N: int, M: int):
    ans = []
    i, j = 0, N + 1
    diffs = set()
    for _ in range(M):
        i += 1
        j -= 1
        while j - i == i + N - j or j - i in diffs or i + N - j in diffs:
            j -= 1
        diffs.add(j - i)
        diffs.add(i + N - j)
        ans.append((i, j))
    for a, b in ans:
        print(a, b)
    



def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  
    M = int(next(tokens))  
    solve(N, M)

if __name__ == '__main__':
    main()

Solution (Python):







def main():
    n , m = map(int , input().split())
    if n % 2 == 0:
        n -= 1
    k = (n + 1) // 2
    j = 1

    while j < k and m > 0:
        print(j , k)
        j += 1
        k -= 1
        m -= 1

    j = (n + 1) // 2 + 1
    k = n

    while j < k and m > 0:
        if k <= n:
            print(j , k)
            m -= 1
        j += 1
        k -= 1
    
    return

if __name__ == "__main__":
    main()

Solution (Python):
n, m = map(int, input().split())
i = 0
c = 0
while (i + 1) + i < (n - i - (i + 1)) and c < m:
    print(i + 1, n - i)
    c += 1
    i += 1
a = n // 2 + n % 2
for i in range(m - c):
    print(a - i - 1, a + i + 1)

Solution (Python):
def main():
    N, M =map(int, input().split())

    if N % 2:
        left = 1
        right = N - 1
        for _ in range(M):
            print(left, right)
            left += 1
            right -= 1
    else:
        left = 1
        right = N - 1
        flag = False
        for _ in range(M):
            if right - left <= N//2:
                flag = True
            
            if flag:
                print(left, right-1)
            else:
                print(left, right)
            
            left += 1
            right -= 1

        
if __name__ == "__main__":
    main()

Solution (Python):
n, m = map(int,input().split())
for i in range(m):
  print(i + 1, 2*m - i + (n%2==0 and 2*(m - i) - 1 >= n//2))

Solution (Python):
n,m= map(int, input().split())
ans=[]
if n%2==1:
    for i in range(m):
        ans.append(i+1)
        ans.append(n-1-i)

else:
    if m<=n//4:
        for i in range(m):
            ans.append(n//2+1+i)
            ans.append(n//2-i)

    else:
        for i in range(m-n//4):
            ans.append(2+i)
            ans.append(n-i)
        for i in range(n//4):
            ans.append(n//2+1+i)
            ans.append(n//2-i)


print(*ans)

Solution (Python):
from collections import Counter
import sys

sys.setrecursionlimit(10 ** 6)

mod = 1000000007
inf = int(1e18)

dx = [0, 1, 0, -1]
dy = [1, 0, -1, 0]


def inverse(a):
    return pow(a, mod - 2, mod)


def usearch(x, a):
    lft = 0
    rgt = len(a) + 1
    while rgt - lft > 1:
        mid = (rgt + lft) // 2
        if a[mid] <= x:
            lft = mid
        else:
            rgt = mid
    return lft


def main():
    n, m = map(int, input().split())
    ans = []
    for i in range(1, (m+1)//2+1):
        if len(ans) == m:
            break
        ans.append([i, m+2-i])

    for i in range(1, (m+1)//2+1):
        if len(ans) == m:
            break
        ans.append([m+1+i, 2*m+2-i])

    for x in ans:
        print(x[0], x[1])

main()

Solution (Python):
from collections import Counter
import sys

sys.setrecursionlimit(10 ** 6)

mod = 1000000007
inf = int(1e18)

dx = [0, 1, 0, -1]
dy = [1, 0, -1, 0]


def inverse(a):
    return pow(a, mod - 2, mod)


def usearch(x, a):
    lft = 0
    rgt = len(a) + 1
    while rgt - lft > 1:
        mid = (rgt + lft) // 2
        if a[mid] <= x:
            lft = mid
        else:
            rgt = mid
    return lft


def main():
    n, m = map(int, input().split())
    ans = []
    for i in range(1, (m+1)//2+1):
        ans.append([i, m+2-i])

    for i in range(1, (m+1)//2+1):
        if len(ans) == m:
            break
        ans.append([m+1+i, 2*m+2-i])

    for x in ans:
        print(x[0], x[1])

main()

Solution (Python):
n,m=map(int,input().split())
k=0
if n%2==1:
  for i in range(m):
    print(i+1,end=" ")
    print(n-i)
elif n%4==0:
  for i in range((n+2)//4):
    if k>=m:
      break
    print(i+1,end=" ")
    print(n-i)
    k+=1
  for i in range((n+2)//4,n//2):
    if k>=m:
      break
    print(i+1,end=" ")
    print(n-i-1)
    k+=1
else:
  for i in range((n+2)//4-1):
    if k>=m:
      break
    print(i+1,end=" ")
    print(n-i)
    k+=1
  for i in range((n+2)//4-1,n//2):
    if k>=m:
      break
    print(i+1,end=" ")
    print(n-i-1)
    k+=1

Solution (Python):
n,k=map(int,input().split())
ans=[]
a=1
b=n
s=set()
for _ in range(k):
  s.add(abs(a-b))
  s.add(abs(n+a-b)%n)
  ans.append([a,b])
  a+=1
  b-=1
  if abs(a-b) in s or abs(n+a-b)%n in s or abs(a-b)==abs(n+a-b):
    b-=1
for i in range(k):
  print(*ans[i])

Solution (Python):
n, m = map(int, input().split())

if n % 2: 
    for i in range(m):
        print(i + 1, n - i)
else: 
    for i in range(m):
        if 1 + 2 * i >= n - 1 - 2 * i:
            l1 = i
            break
        m -= 1
        print(i + 1, n - i)

    for i in range(m):
        if i + 1 + l1 >= n - i - l1 - 1:
            raise Exception()
        print(i + 1 + l1, n - i - l1 - 1)

Solution (Python):
N, M = map(int, input().split())

M_MAX = (N - 1) // 2

pos = 1
size = M_MAX
i = 0
while i < M and size > 0:
    print(pos, pos + size)
    pos += 1
    i += 1
    size -= 2

pos = 1 + M_MAX + 1
size = M_MAX - 1
while i < M and size > 0:
    print(pos, pos + size)
    pos += 1
    i += 1
    size -= 2

Solution (Python):
N, M = map(int, input().split())
matches = []
i = 1
l = N // 2 - 1 if N % 2 == 0 else N // 2
while len(matches) < M:
    if l <= 0:
        i = N // 2 + 1 if N % 2 == 0 else N // 2 + 2
        l = N // 2 - 2 if N % 2 == 0 else N // 2 - 1
        continue
    matches.append((i, i+l))
    i += 1; l -= 2
for a, b in matches: print(a, b)

Solution (Python):
n,m=map(int,input().split())
l=m//2
for i in range(l):
    print(1+i,1+2*l-i)
for j in range(m-l):
    print(1+2*l+1+j,2*m+1-j)

Solution (Python):
N, M = map(int, input().split())
order = [i for i in range(2, N+1)]
reverse = order[::-1]
d = 0
for i in range(M):
    if N%4 == 0 and reverse[i] - order[i] == N//2:
        d = 1
    if N%2 == 0 and i == (N//2-1) //2:
        d = 1
    print(order[i+d], reverse[i])

Solution (Python):
def main():
    d = 0
    for i in range(M):
        if N%4 == 0 and reverse[i] - order[i] == N//2:
            d = 1
        if N%2 == 0 and i == (N//2-1) //2:
            d = 1
        print(order[i+d], reverse[i])

N, M = map(int, input().split())
order = [i for i in range(2, N+1)]
reverse = order[::-1]
main()

Solution (Python):
def odd():
    for i in range(M):
        print(order[i], reverse[i])

def multipule4():
    d = 0
    for i in range(M):
        if reverse[i] - order[i] == N//2:
            d = 1
        print(order[i+d], reverse[i])

def even():
    d = 0
    for i in range(M):
        if i == (N//2-1) //2:
            d = 1
        print(order[i+d], reverse[i])
    

N, M = map(int, input().split())
order = [i for i in range(2, N+1)]
reverse = order[::-1]

if N%2 != 0:
    odd()
elif N%4 == 0:
    multipule4()
else:
    even()

Solution (Python):
N, M = map(int, input().split())

if N % 2 == 1:
    for i in range(M):
        j = N - i
        print(f'{i + 1} {j}')
else:
    for i in range(M):
        j = N - i
        if i < M / 2:
            print(f'{i + 1} {j}')
        else:
            print(f'{i + 1} {j - 1}')

Solution (Python):

import sys
sys.setrecursionlimit(10**8)
INF = float("inf")


def solve(N: int, M: int):
    

    
    
    ans = []

    if N % 2 == 0:
        
        a, b = (0, N//2-1)
        
        while a < b:
            ans.append((a+1, b+1))
            a += 1
            b -= 1
        
        a, b = (N//2, N-2)
        while a < b:
            ans.append((a+1, b+1))
            a += 1
            b -= 1
    if N % 2 == 1:
        
        a, b = (0, N//2)
        while a < b:
            ans.append((a+1, b+1))
            a += 1
            b -= 1
        
        a, b = (N//2+1, N-1)
        while a < b:
            ans.append((a+1, b+1))
            a += 1
            b -= 1
    for i in range(M):
        print(*ans[i], sep=" ")
    return


def main():

    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  
    M = int(next(tokens))  
    solve(N, M)


if __name__ == '__main__':
    main()

Solution (Python):
n,m = map(int,input().split())
if n % 2 == 1:ans = [[1+i,n-i] for i in range(n//2)]
else:ans = [[1+i,n-i] for i in range(n//4)]+[[n//2+1+i,n//2-1-i] for i in range(n//2-n//4-1)]
for i in range(m):print(ans[i][0],ans[i][1])

Solution (Python):
n,m = map(int,input().split())
if n % 2 == 1:
    ans = [[1+i,n-i] for i in range(n//2)]
else:
    ans = [[1+i,n-i] for i in range(n//4)]+[[n//2+1+i,n//2-1-i] for i in range(n//2-n//4-1)]
for i in range(m):
    print(ans[i][0],ans[i][1])

Solution (Python):
from sys import setrecursionlimit, exit
setrecursionlimit(1000000000)

def main():
    n, m = map(int, input().split())
    a = 1
    d = n - 1
    for _ in range(m):
        if d % 2 == 1 and (d == n // 2 or d == n // 2 - 1):
            d -= 1
        print(a, a + d)
        a += 1
        d -= 2

main()

Solution (Python):
from heapq import heappush, heappop, heapify
from collections import deque, defaultdict, Counter
import itertools
from itertools import permutations, combinations, accumulate, product, combinations_with_replacement
import sys
import bisect
import string
import math
import time


def I(): return int(input())


def S(): return input()


def MI(): return map(int, input().split())


def MS(): return map(str, input().split())


def LI(): return [int(i) for i in input().split()]


def LI_(): return [int(i)-1 for i in input().split()]


def StoI(): return [ord(i)-97 for i in input()]


def ItoS(nn): return chr(nn+97)


def input(): return sys.stdin.readline().rstrip()


def debug(table, *args):
    ret = []
    for name, val in table.items():
        if val in args:
            ret.append('{}: {}'.format(name, val))
    print(' | '.join(ret), file=sys.stderr)


yn = {False: 'No', True: 'Yes'}
YN = {False: 'NO', True: 'YES'}
MOD = 10**9+7
inf = float('inf')
IINF = 10**10
l_alp = string.ascii_lowercase
u_alp = string.ascii_uppercase
ts = time.time()
sys.setrecursionlimit(10**6)
nums = ['1', '2', '3', '4', '5', '6', '7', '8', '9', '10']

show_flg = False



def main():
    N, M = MI()

    if N % 2 == 1:
        pairs = []
        for i in range(N//2):
            pairs.append((i+1, N-i))

        
        for i in range(M):
            print(*pairs[i])
            
            
    else:
        pairs = []
        for i in range(N//2//2):
            pairs.append((i+1, N-i))

        for i in range(N//2//2+1, N//2):
            pairs.append((i+1, N-i+1))

        
        for i in range(M):
            print(*pairs[i])
            
            


if __name__ == '__main__':
    main()

Solution (Python):
import math

bl=input().split()
n=int(bl[0])
s=int(bl[1])

for a in range(math.ceil(s/2)):
  print(str(a+1)+" "+str(s-a+1))
for b in range(math.floor(s/2)):
  print(str(s+b+2)+" "+str(2*s-b+1))

Solution (Python):
n,m=map(int, input().split())
if m%2==1:
    for i in range(m//2):
        print(i+1,m-i)
    for i in range(m//2+1):
        print(m+i+1,2*m+1-i)
else:
    for i in range(m//2):
        print(i+1,m+1-i)
    for i in range(m//2):
        print(m+i+2,2*m+1-i)

Solution (Python):
N, M = map(int, input().split())

res = []

if N % 2 == 0:
    x = 0
    for i in range(N // 2 // 2):
        res.append((x + 1, (x + 2 * i + 1) % N + 1))
        x -= 1
        x %= N
    for i in range((N // 2 - 1) // 2):
        res.append((x + 1, (x - (N // 2 - 1) // 2 * 2 + 2 * i) % N + 1))
        x -= 1
        x %= N

else:
    for i in range(N // 2):
        res.append((i + 1, N - i - 1))

for i in range(M):
    a, b = res[i]
    print(a, b)

Solution (Python):
N,M=map(int,input().split())
venue=[]
if N%2==0:
    l=1
    r=N//2
    while l<r:
        venue.append([l,r])
        l+=1
        r-=1
    l=N//2+1
    r=N-1
    while l<r:
        venue.append([l,r])
        l+=1
        r-=1
else:
    l=1
    r=N//2
    while l<r:
        venue.append([l,r])
        l+=1
        r-=1
    l=N//2+1
    r=N
    while l<r:
        venue.append([l,r])
        l+=1
        r-=1
for a,b in venue:
    M-=1
    print(a,b)
    if M==0:
        break

Solution (Python):
N,M = map(int,input().split())

a = 0
b = M+1

for i in range(M//2):
    a += 1
    b -= 1
    print(a,b)

a = M
b = 2*M+2

for i in range((M+1)//2):
    a += 1
    b -= 1
    print(a,b)

Solution (Python):
N, M = map(int, input().split())
if N%2==0:
    for i in range(M):
        x = 0
        if i>=M/2:
            x = 1
        a = 1 + i
        b = N - i
        print(a+x, b)
else:
    n = (N//2)*2
    for i in range(M):
        a = 1 + i
        b = a + n - (2*i+1)
        print(a, b)

Solution (Python):
n,m=map(int,input().split())
for i in range(0,m):
  if n-2*i-1>n/2 or n%2==1 :
    print(i+1,n-i)
  else:
    print(i+1,n-i-1)

Solution (Python):
n,m=map(int,input().split())
k=m//2
for i in range (0,k):
    a=i+1
    b=2*k+1-i
    print (a,b)
c=2*k+2
k=(m+1)//2
j=1

for i in range (c,c+k):
    a=i
    b=c+2*k-j
    j+=1
    print(a,b)

Solution (Python):


(n, m) = map(int, input().split())

if m % 2 == 1:
    
    c = m // 2
    for i in range(c):
        print(i + 1, c * 2 + 1 - i)
        
    
    f = (m // 2) * 2 + 2
    c = m // 2 + 1
    for i in range(c):
        print(f + i, f + c * 2 - 1 - i)
              
else:
    
    c = m // 2
    for i in range(c):
        print(i + 1, c * 2 + 1 - i)
    
    f = (m // 2) * 2 + 2
    c = m // 2
    for i in range(c):
        print(f + i, f + c * 2 - 1 - i)

Solution (Python):

N, M = map(int, input().split())


ans = []

t = 1
for _ in range(M//2):
    ans.append((t, M-t+1))
    t += 1

t = M+1
for _ in range(-(-M//2)):
    ans.append((t, M*3+2-t))
    t += 1


[print(a, b) for a, b in ans]

Solution (Python):
import math

N, M = map(int, input().split())

if N%2 == 1:
  a = 1
  b = N
  for i in range(M):
    print(a,b)
    a += 1
    b -= 1
else:
  m = N//2 - 1
  a = N//4
  b = a + 1
  c = N//2 + N//4
  d = c + 2
  for i in range(M):
    if i%2 == 0:
      print(a,b)
      a -= 1
      b += 1
    else:
      print(c,d)
      c -= 1
      d += 1

Solution (Python):
N, M = map(int, input().split())

odd_head, odd_tail = 1, 0
even_head, even_tail = 0, 0

if M & 1:
    odd_tail = M + 1
    even_head = M + 2
    even_tail = M + 2 + M - 1
else:
    odd_tail = 1 + (M - 1)
    even_head = M + 1
    even_tail = M + 1 + M

while odd_tail - odd_head > 0:
    print(odd_head, odd_tail)
    odd_head += 1
    odd_tail -= 1

while even_tail - even_head > 0:
    print(even_head, even_tail)
    even_head += 1
    even_tail -= 1

Solution (Python):
N, M = map(int, input().split())


if M & 1:
    odd_head = 1
    odd_tail = M + 1
    even_head = M + 2
    even_tail = M + 2 + M - 1
    while odd_tail - odd_head > 0:
        print(odd_head, odd_tail)
        odd_head += 1
        odd_tail -= 1

    while even_tail - even_head > 0:
        print(even_head, even_tail)
        even_head += 1
        even_tail -= 1

else:
    odd_head = 1
    odd_tail = 1 + (M - 1)
    even_head = M + 1
    even_tail = M + 1 + M
    while odd_tail - odd_head > 0:
        print(odd_head, odd_tail)
        odd_head += 1
        odd_tail -= 1

    while even_tail - even_head > 0:
        print(even_head, even_tail)
        even_head += 1
        even_tail -= 1