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 C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Collections.Immutable;
using System.Diagnostics;
using System.Runtime.CompilerServices;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.Intrinsics.X86;
using System.Text;
using static Solve.Methods;
using static Solve.Input;
using static Solve.Output;
using static System.Math;

namespace Solve
{
    public partial class Solver
    {
        public void Main() {
            var (N, M) = Int;

            for (int i = 1; i <= M; ++i) {
                if (N % 2 == 1) {
                    prints(i, N - i);
                } else {
                    prints(i, N - i + 1);
                }
            }
        }
        

        const int MOD = 1_000_000_007;
    }
    public static class Methods
    {
        [MethodImpl(256)]
        public static bool Assert(in bool b, in string message = null) =>
            b ? true : throw new Exception(message ?? "Assert failed.");
        [MethodImpl(256)]
        public static string JoinSpace<T>(this IEnumerable<T> source) => source.Join(" ");
        [MethodImpl(256)]
        public static string JoinEndline<T>(this IEnumerable<T> source) => source.Join("\n");
        [MethodImpl(256)]
        public static string Join<T>(this IEnumerable<T> source, string s) =>
            string.Join(s, source);
        [MethodImpl(256)]
        public static string Join<T>(this IEnumerable<T> source, char c) =>
            string.Join(c.ToString(), source);
        public static long Gcd(long a, long b) {
            while (true) {
                if (a < b) (a, b) = (b, a);
                if (a % b == 0) return b;
                var x = a;
                a = b;
                b = x % b;
            }
        }
        public static long Lcm(long a, long b) => a / Gcd(a, b) * b;
        public static bool IsPrime(long value) {
            if (value <= 1) return false;
            for (long i = 2; i * i <= value; ++i)
                if (value % i == 0)
                    return false;
            return true;
        }
        public static long PowMod(long a, long b, long p) {
            long res = 1;
            while (b > 0) {
                if (b % 2 != 0) res = res * a % p;
                a = a * a % p;
                b >>= 1;
            }

            return res;
        }
        public static IEnumerable<long> Factors(long n) {
            Assert(n >= 0, "n must be greater than 0.");
            for (long i = 1; i * i <= n; ++i) {
                long div = DivRem(n, i, out long rem);
                if (rem > 0) continue;
                yield return div;
                if (i != div) yield return i;
            }
        }
        public static IEnumerable<int> Factors(int n) => Factors((long) n).Select(Convert.ToInt32);

        [MethodImpl(256)] public static int DivCeil(int a, int b) => (a + b - 1) / b;
        [MethodImpl(256)] public static long DivCeil(long a, long b) => (a + b - 1) / b;
        public static IEnumerable<T[]> Permutations<T>(IEnumerable<T> src) {
            var ret = new List<T[]>();
            Search(ret, new Stack<T>(), src.ToArray());
            return ret;

            static void Search(ICollection<T[]> perms, Stack<T> stack, T[] a) {
                int N = a.Length;
                if (N == 0) perms.Add(stack.Reverse().ToArray());
                else {
                    var b = new T[N - 1];
                    Array.Copy(a, 1, b, 0, N - 1);
                    for (int i = 0; i < a.Length; ++i) {
                        stack.Push(a[i]);
                        Search(perms, stack, b);
                        if (i < b.Length) b[i] = a[i];
                        stack.Pop();
                    }
                }
            }
        }
        public static long BinarySearch(long low,
            long high,
            Func<long, bool> expression
        ) {
            while (low < high) {
                long middle = (high - low) / 2 + low;
                if (!expression(middle))
                    high = middle;
                else
                    low = middle + 1;
            }

            return high;
        }
        public static int LowerBound<T>(T[] arr,
            int start,
            int end,
            T value,
            IComparer<T> comparer
        ) {
            int low = start;
            int high = end;
            while (low < high) {
                var mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) < 0)
                    low = mid + 1;
                else
                    high = mid;
            }

            return low;
        }
        public static int LowerBound<T>(T[] arr, T value)
            where T : IComparable {
            return LowerBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        }
        public static int UpperBound<T>(T[] arr,
            int start,
            int end,
            T value,
            IComparer<T> comparer
        ) {
            int low = start;
            int high = end;
            while (low < high) {
                var mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) <= 0)
                    low = mid + 1;
                else
                    high = mid;
            }

            return low;
        }
        public static int UpperBound<T>(T[] arr, T value) {
            return UpperBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        }
        [MethodImpl(256)]
        public static IEnumerable<TResult> Repeat<TResult>(TResult value,
            int count
        ) =>
            Enumerable.Repeat(value, count);
        [MethodImpl(256)]
        public static string AsString(this IEnumerable<char> source) =>
            new string(source.ToArray());
        [MethodImpl(256)]
        public static IEnumerable<long> CumSum(this IEnumerable<long> source) {
            long sum = 0;
            foreach (var item in source)
                yield return sum += item;
        }
        [MethodImpl(256)]
        public static IEnumerable<int> CumSum(this IEnumerable<int> source) {
            int sum = 0;
            foreach (var item in source)
                yield return sum += item;
        }
        [MethodImpl(256)] public static bool IsIn<T>(this T value, T l, T r)
            where T : IComparable<T> =>
            l.CompareTo(r) > 0
                ? throw new ArgumentException()
                : l.CompareTo(value) <= 0 && value.CompareTo(r) < 0;
        [MethodImpl(256)]
        public static bool IsIn(this in int value, in Range range) =>
            value.IsIn(range.Start.Value, range.End.Value);
        [MethodImpl(256)]
        public static bool IsIn(this in Index value, in Range range) =>
            value.IsFromEnd &&
            value.Value.IsIn(range.Start.Value, range.End.Value);
        [MethodImpl(256)]
        public static IEnumerable<int> Range(int start, int end, int step = 1) {
            for (var i = start; i < end; i += step) yield return i;
        }
        [MethodImpl(256)] public static IEnumerable<int> Range(int end) => Range(0, end);
        [MethodImpl(256)]
        public static IEnumerable<int> Range(Range range, int step = 1) =>
            Range(range.Start.Value, range.End.Value, step);
        [MethodImpl(256)] public static T[] Sort<T>(this T[] arr)
            where T : IComparable<T> {
            var array = arr[..];
            Array.Sort(array);
            return array;
        }
        [MethodImpl(256)]
        public static T[] Sort<T, U>(this T[] arr, Func<T, U> selector)
            where U : IComparable<U> {
            var array = arr[..];
            Array.Sort(array, (a, b) => selector(a).CompareTo(selector(b)));
            return array;
        }
        [MethodImpl(256)] public static T[] SortDescending<T>(this T[] arr)
            where T : IComparable<T> {
            var array = arr[..];
            Array.Sort(array, (a, b) => b.CompareTo(a));
            return array;
        }
        [MethodImpl(256)]
        public static T[] SortDescending<T, U>(this T[] arr,
            Func<T, U> selector
        ) where U : IComparable<U> {
            var array = arr[..];
            Array.Sort(array, (a, b) => selector(b).CompareTo(selector(a)));
            return array;
        }
        public static T[] Unique<T>(this IEnumerable<T> arr) {
            var source = arr.ToArray();
            var ret = new List<T>(source.Length);
            var set = new SortedSet<T>();
            ret.AddRange(source.Where(val => set.Add(val)));

            return ret.ToArray();
        }
        [MethodImpl(256)] public static bool chmin<T>(ref T a, T b)
            where T : IComparable<T> {
            if (a.CompareTo(b) > 0) {
                a = b;
                return true;
            }

            return false;
        }
        [MethodImpl(256)] public static bool chmax<T>(ref T a, T b)
            where T : IComparable<T> {
            if (a.CompareTo(b) < 0) {
                a = b;
                return true;
            }

            return false;
        }
        [MethodImpl(256)]
        public static T[][] JaggedArray2D<T>(int a,
            int b,
            T defaultValue = default
        ) {
            var ret = new T[a][];
            for (int i = 0; i < a; ++i)
                ret[i] = Enumerable.Repeat(defaultValue, b).ToArray();
            return ret;
        }
        [MethodImpl(256)]
        public static T[,] Array2D<T>(int a, int b, T defaultValue = default) {
            var ret = new T[a, b];
            for (int i = 0; i < a; ++i)
            for (int j = 0; j < b; ++j)
                ret[i, j] = defaultValue;
            return ret;
        }
        [MethodImpl(256)] public static T[,] To2DArray<T>(this T[][] array) {
            if (!array.Any()) return new T[0, 0];

            int len = array[0].Length;
            if (array.Any(x => x.Length != len))
                throw new ArgumentException("array の各要素の長さが異なります。",
                    nameof(array));

            var ret = new T[array.Length, len];
            for (int i = 0; i < array.Length; ++i)
            for (int j = 0; j < len; ++j)
                ret[i, j] = array[i][j];
            return ret;
        }
        [MethodImpl(256)] public static T Min<T>(params T[] col) => col.Min();
        [MethodImpl(256)] public static T Max<T>(params T[] col) => col.Max();
        [MethodImpl(256)]
        public static IEnumerable<(T, int)> WithIndex<T>(
            this IEnumerable<T> source
        ) =>
            source.Select((x, i) => (x, i));
        [MethodImpl(256)] public static (T, U, V)[] Zip<T, U, V>(
            IReadOnlyCollection<T> t,
            IReadOnlyCollection<U> u,
            IReadOnlyCollection<V> v
        ) {
            Assert(t.Count == u.Count && u.Count == v.Count);
            return t.Zip(u, (a, b) => (a, b))
                .Zip(v, (tuple, c) => (tuple.Item1, tuple.Item2, c)).ToArray();
        }
        [MethodImpl(256)]
        public static void rep(in int start, in int end, Action<int> func) {
            for (int i = start; i < end; ++i) func(i);
        }
        [MethodImpl(256)]
        public static void rep(in int end, Action<int> func) => rep(0, end, func);
        [MethodImpl(256)]
        public static void rep1(in int end, Action<int> func) => rep(1, end + 1, func);
        [MethodImpl(256)]
        public static void repr(in int end, Action<int> func) {
            for (int i = end - 1; i >= 0; --i) func(i);
        }
        [MethodImpl(256)]
        public static void each<T>(this IEnumerable<T> source, Action<T> func) {
            foreach (var item in source) func(item);
        }
        [MethodImpl(256)]
        public static void eachWithIndex<T>(this IEnumerable<T> source,
            Action<T, int> func
        ) {
            int index = 0;
            foreach (var item in source) func(item, index++);
        }
        [MethodImpl(256)] public static int bit(in int x) => 1 << x;
        [MethodImpl(256)] public static long bitl(in int x) => 1L << x;
    }
    public static class Caluclation
    {
        [MethodImpl(256)] public static int Addition(int a, int b) => a + b;
        [MethodImpl(256)] public static long Addition(long a, long b) => a + b;
        [MethodImpl(256)] public static double Addition(double a, double b) => a + b;
        [MethodImpl(256)] public static int Xor(int a, int b) => a ^ b;
        [MethodImpl(256)] public static long Xor(long a, long b) => a ^ b;
        [MethodImpl(256)] public static int Multiplication(int a, int b) => a * b;
        [MethodImpl(256)] public static long Multiplication(long a, long b) => a * b;
    }
    public class UnorderedMap<T, U> : Dictionary<T, U>
    {
        public new U this[T k] {
            get =>
                TryGetValue(k, out var v) ? v : base[k] = default;
            set =>
                base[k] = value;
        }
    }
    public class Map<T, U> : SortedDictionary<T, U>
    {
        public new U this[T k] {
            get =>
                TryGetValue(k, out var v) ? v : base[k] = default;
            set =>
                base[k] = value;
        }
    }
    public class Scanner<T>
    {
        public T r => next<T>();
        public T next() => r;

        private IEnumerable<T> enumerable(int N) {
            for (int i = 0; i < N; ++i) yield return r;
        }

        public T[] array(in int N) => enumerable(N).ToArray();
        public List<T> list(in int N) => enumerable(N).ToList();
        public T[,] array2d(in int N, in int M) => next2DArray<T>(N, M);
        public T[][] listArray(in int n) {
            var ret = new T[n][];
            for (int i = 0; i < n; i++) ret[i] = array(next<int>());
            return ret;
        }

        public void Deconstruct(out T _1, out T _2) => (_1, _2) = (r, r);
        public void Deconstruct(out T _1, out T _2, out T _3) => (_1, _2, _3) = (r, r, r);
        public void Deconstruct(out T _1, out T _2, out T _3, out T _4) =>
            (_1, _2, _3, _4) = (r, r, r, r);
        public void Deconstruct(out T _1,
            out T _2,
            out T _3,
            out T _4,
            out T _5
        ) =>
            (_1, _2, _3, _4, _5) = (r, r, r, r, r);
        public void Deconstruct(out T _1,
            out T _2,
            out T _3,
            out T _4,
            out T _5,
            out T _6
        ) =>
            (_1, _2, _3, _4, _5, _6) = (r, r, r, r, r, r);
        public void Deconstruct(out T _1,
            out T _2,
            out T _3,
            out T _4,
            out T _5,
            out T _6,
            out T _7
        ) =>
            (_1, _2, _3, _4, _5, _6, _7) = (r, r, r, r, r, r, r);
        public void Deconstruct(out T _1,
            out T _2,
            out T _3,
            out T _4,
            out T _5,
            out T _6,
            out T _7,
            out T _8
        ) =>
            (_1, _2, _3, _4, _5, _6, _7, _8) = (r, r, r, r, r, r, r, r);
        public void Deconstruct(
            out T _1,
            out T _2,
            out T _3,
            out T _4,
            out T _5,
            out T _6,
            out T _7,
            out T _8,
            out T _9
        ) =>
            (_1, _2, _3, _4, _5, _6, _7, _8, _9) = (r, r, r, r, r, r, r, r, r);
        public void Deconstruct(
            out T _1,
            out T _2,
            out T _3,
            out T _4,
            out T _5,
            out T _6,
            out T _7,
            out T _8,
            out T _9,
            out T _10
        ) =>
            (_1, _2, _3, _4, _5, _6, _7, _8, _9, _10) =
            (r, r, r, r, r, r, r, r, r, r);
        
        public static implicit operator T(Scanner<T> sc) => sc.r;
    }
    public static class Input
    {
        private const char _separator = ' ';
        private static readonly Queue<string> _input = new Queue<string>();
        private static readonly StreamReader sr =
#if FILE
            new StreamReader("in.txt");
#else
            new StreamReader(Console.OpenStandardInput());
#endif

        public static string ReadLine => sr.ReadLine();
        public static string ReadStr => Read;
        public static int ReadInt => int.Parse(Read);
        public static long ReadLong => long.Parse(Read);
        public static ulong ReadULong => ulong.Parse(Read);
        public static double ReadDouble => double.Parse(Read);
        public static BigInteger ReadBigInteger => BigInteger.Parse(Read);

        public static string Read {
            get {
                if (_input.Any()) return _input.Dequeue();

                foreach (var val in sr.ReadLine().Split(_separator))
                    _input.Enqueue(val);

                return _input.Dequeue();
            }
        }

        public static string next() => Read;
        public static T next<T>() =>
            default(T) switch {
                sbyte _ => (T) (object) (sbyte) ReadInt,
                short _ => (T) (object) (short) ReadInt,
                int _ => (T) (object) ReadInt,
                long _ => (T) (object) ReadLong,
                byte _ => (T) (object) (byte) ReadULong,
                ushort _ => (T) (object) (ushort) ReadULong,
                uint _ => (T) (object) (uint) ReadULong,
                ulong _ => (T) (object) ReadULong,
                float _ => (T) (object) (float) ReadDouble,
                double _ => (T) (object) ReadDouble,
                string _ => (T) (object) ReadStr,
                char _ => (T) (object) ReadStr[0],
                BigInteger _ => (T) (object) ReadBigInteger,
                _ => typeof(T) == typeof(string)
                    ? (T) (object) ReadStr
                    : throw new NotSupportedException(),
            };
        public static (T, U) next<T, U>() => (next<T>(), next<U>());
        public static (T, U, V) next<T, U, V>() => (next<T>(), next<U>(), next<V>());
        public static (T, U, V, W) next<T, U, V, W>() =>
            (next<T>(), next<U>(), next<V>(), next<W>());
        public static (T, U, V, W, X) next<T, U, V, W, X>() =>
            (next<T>(), next<U>(), next<V>(), next<W>(), next<X>());

        public static T[] nextArray<T>(in int size) {
            var ret = new T[size];
            for (int i = 0; i < size; ++i) ret[i] = next<T>();
            return ret;
        }
        public static T[,] next2DArray<T>(int n, in int m) {
            var ret = new T[n, m];
            for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j)
                ret[i, j] = next<T>();
            return ret;
        }
        public static (T[], U[]) nextArray<T, U>(in int size) {
            var ret1 = new T[size];
            var ret2 = new U[size];
            for (int i = 0; i < size; ++i) (ret1[i], ret2[i]) = next<T, U>();
            return (ret1, ret2);
        }
        public static (T[], U[], V[]) nextArray<T, U, V>(in int size) {
            var ret1 = new T[size];
            var ret2 = new U[size];
            var ret3 = new V[size];
            for (int i = 0; i < size; ++i)
                (ret1[i], ret2[i], ret3[i]) = next<T, U, V>();
            return (ret1, ret2, ret3);
        }
    }
    public static class Output
    {
        [MethodImpl(256)] public static void print() => Console.WriteLine();
        [MethodImpl(256)]
        public static void print(in string s, bool endline = true) {
            if (endline) Console.WriteLine(s);
            else Console.Write(s);
        }
        [MethodImpl(256)]
        public static void print(in int v, bool endline = true) {
            if (endline) Console.WriteLine(v);
            else Console.Write(v);
        }
        [MethodImpl(256)]
        public static void print(in long v, bool endline = true) {
            if (endline) Console.WriteLine(v);
            else Console.Write(v);
        }
        [MethodImpl(256)]
        public static void print(in ulong v, bool endline = true) {
            if (endline) Console.WriteLine(v);
            else Console.Write(v);
        }
        [MethodImpl(256)] public static void print(in bool b) => PrintBool(b);
        [MethodImpl(256)] public static void print(in object v) => Console.WriteLine(v);
        [MethodImpl(256)]
        public static void print<T>(in IEnumerable<T> array,
            string separator = " "
        ) =>
            Console.WriteLine(array.Join(separator));
        [MethodImpl(256)] public static void prints<T>(params T[] t) => print(t);
        
#if LOCAL
        [MethodImpl(256)]
        public static void debug<T>(in T value, bool endline = true) {
            if (endline) Console.WriteLine(value);
            else Console.Write(value);
        }
#else
        public static void debug(params object[] obj) { }
#endif

        private static void PrintBool(in bool val,
            in string yes = null,
            in string no = null
        ) =>
            print(val ? yes ?? _yes : no ?? _no);
        private static string _yes = "Yes", _no = "No";

        public static void SetYesNoString(in YesNoType t) => (_yes, _no) = YesNoString[t];
        public static void SetYesNoString(in string yes, in string no) => (_yes, _no) = (yes, no);

        private static readonly Dictionary<YesNoType, (string yes, string no)>
            YesNoString =
                new Dictionary<YesNoType, (string yes, string no)>() {
                    {YesNoType.Yes_No, ("Yes", "No")},
                    {YesNoType.YES_NO, ("YES", "NO")},
                    {YesNoType.Upper, ("YES", "NO")},
                    {YesNoType.yes_no, ("yes", "no")},
                    {YesNoType.Lower, ("yes", "no")},
                    {YesNoType.Possible_Impossible, ("Possible", "Impossible")},
                    {YesNoType.Yay, ("Yay!", ":(")},
                };

        public static readonly (string yes, string no)
            YN_Possible = ("Possible", "Impossible"),
            YN_lower = ("yes", "no"),
            YN_upper = ("YES", "NO"),
            YN_Yay = ("Yay!", ":(");

        public static void Yes() => print(_yes);
        public static void No() => print(_no);

        public static object cout {
            set => Console.WriteLine(value);
        }
#if LOCAL
        public static object dout {
            set => Console.WriteLine(value);
        }
#else
        public static object dout { set { } }
#endif
        public static object cerr {
            set => Console.Error.WriteLine(value);
        }

        public const string endl = "\n";

        public enum YesNoType { Yes_No, YES_NO, Upper, yes_no, Lower, Possible_Impossible, Yay }
    }
    public class Program
    {
        public static void Main(string[] args) {
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(sw);
            new Solver().Main();
            Console.Out.Flush();
        }
    }
    partial class Solver
    {
        readonly Scanner<int> Int;
        readonly Scanner<long> Long;
        readonly Scanner<string> String;
        public Solver() =>
            (Int, String, Long) = (new Scanner<int>(), new Scanner<string>(),
                new Scanner<long>());
        const int INF = 1000000010;
        const long LINF = 1000000000000000100;
        const double EPS = 1e-9;
        public static readonly int[] dx = {-1, 0, 0, 1}, dy = {0, 1, -1, 0};
    }
}