Problem:
Score : 500 points

Problem Statement

We have N logs of lengths A_1,A_2,\cdots A_N.

We can cut these logs at most K times in total. When a log of length L is cut at a point whose distance from an end of the log is t (0<t<L), it becomes two logs of lengths t and L-t.

Find the shortest possible length of the longest log after at most K cuts, and print it after rounding up to an integer.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq K \leq 10^9

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \cdots A_N

Output

Print an integer representing the answer.

Sample Input 1

2 3
7 9

Sample Output 1

4

First, we will cut the log of length 7 at a point whose distance from an end of the log is 3.5, resulting in two logs of length 3.5 each.

Next, we will cut the log of length 9 at a point whose distance from an end of the log is 3, resulting in two logs of length 3 and 6.

Lastly, we will cut the log of length 6 at a point whose distance from an end of the log is 3.3, resulting in two logs of length 3.3 and 2.7.

In this case, the longest length of a log will be 3.5, which is the shortest possible result. After rounding up to an integer, the output should be 4.

Sample Input 2

3 0
3 4 5

Sample Output 2

5

Sample Input 3

10 10
158260522 877914575 602436426 24979445 861648772 623690081 433933447 476190629 262703497 211047202

Sample Output 3

292638192

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

using System;
using System.IO;
using System.Linq;
using System.Collections.Generic;
using static System.Math;
using static System.Console;
using static System.Linq.Enumerable;
using static System.Numerics.BitOperations;

namespace ABC174
{
    class SolverE
    {
        static void Main()
        {
            SetOut(new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false});
            new SolverE().Solve();
            Out.Flush();
        }

        public void Solve()
        {
            (long N, long K) = Get.Tuple<long,long>();
            long[] A = Get.Longs();
            
            var q = new PriorityQueue<Log>((int)N, 1);
            for (int i = 0; i < N; i++)
            {
                q.Push(new Log(i, A[i], A[i]));
            }
        
            for(int i=0; i < K; i++){
                Log longest = q.Pop();
                longest.cut++;
                if(longest.length % longest.cut != 0){
                    longest.length = longest.defaultLength / (longest.cut) + 1;
                }else{
                    longest.length = longest.defaultLength / (longest.cut);
                }
                
                // if(longest.defaultLength % longest.cut != 0){
                //     longest.length++;
                // }
                q.Push(longest);
            }

            long max = 0;
            foreach(Log l in q){
                max = Max(max, l.length);
            }
            WriteLine(max);

            
        }

        class Log : IComparable{
            public long num;
            public long defaultLength;
            public long length;
            public long cut = 0;

            public Log(long _num, long _length, long _defaultLength){
                this.num = _num;
                this.length = _length;
                defaultLength = _defaultLength;
            }

            public int CompareTo(Object otherObj){
                if( otherObj is Log other){
                    return length.CompareTo(other.length);
                }
                return -1;
            }
        }


        public class PriorityQueue<T> where T: IComparable
        {
            private IComparer<T> _comparer = null;
            private int _type = 0;

            private T[] _heap;
            private int _sz = 0;

            private int _count = 0;

            /// <summary>
            /// Priority Queue with custom comparer
            /// </summary>
            public PriorityQueue(int maxSize, IComparer<T> comparer)
            {
                _heap = new T[maxSize];
                _comparer = comparer;
            }

            /// <summary>
            /// Priority queue
            /// </summary>
            /// <param name="maxSize">max size</param>
            /// <param name="type">0: asc, 1:desc</param>
            public PriorityQueue(int maxSize, int type = 0)
            {
                _heap = new T[maxSize];
                _type = type;
            }

            private int Compare(T x, T y)
            {
                if (_comparer != null) return _comparer.Compare(x, y);
                return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
            }

            public void Push(T x)
            {
                _count++;

                //node number
                var i = _sz++;

                while (i > 0)
                {
                    //parent node number
                    var p = (i - 1) / 2;

                    if (Compare(_heap[p], x) <= 0) break;

                    _heap[i] = _heap[p];
                    i = p;
                }

                _heap[i] = x;
            }

            public T Pop()
            {
                _count--;

                T ret = _heap[0];
                T x = _heap[--_sz];

                int i = 0;
                while (i * 2 + 1 < _sz)
                {
                    //children
                    int a = i * 2 + 1;
                    int b = i * 2 + 2;

                    if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

                    if (Compare(_heap[a], x) >= 0) break;

                    _heap[i] = _heap[a];
                    i = a;
                }

                _heap[i] = x;

                return ret;
            }

            public int Count()
            {
                return _count;
            }

            public T Peek()
            {
                return _heap[0];
            }

            public bool Contains(T x)
            {
                for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
                return false;
            }

            public void Clear()
            {
                while (this.Count() > 0) this.Pop();
            }

            public IEnumerator<T> GetEnumerator()
            {
                var ret = new List<T>();

                while (this.Count() > 0)
                {
                    ret.Add(this.Pop());
                }

                foreach (var r in ret)
                {
                    this.Push(r);
                    yield return r;
                }
            }

            public T[] ToArray()
            {
                T[] array = new T[_sz];
                int i = 0;

                foreach (var r in this)
                {
                    array[i++] = r;
                }

                return array;
            }
        }



        private static class Get
        {
            public static string Str() => ReadLine().Trim();
            public static int Int() => int.Parse(Str());
            public static long Long() => long.Parse(Str());
            public static double Double() => double.Parse(Str());
            public static string[] Strs() => Str().Split(' ', StringSplitOptions.RemoveEmptyEntries);
            public static int[] Ints() => Strs().Select(int.Parse).ToArray();
            public static long[] Longs() => Strs().Select(long.Parse).ToArray();
            public static double[] Doubles() => Strs().Select(double.Parse).ToArray();
            static bool TypeEq<T,U>() => typeof(T).Equals(typeof(U));
            static T TypeConv<T,U>(U u) => (T)Convert.ChangeType(u, typeof(T));
            static T TypeConv<T>(string s) => TypeEq<T, int>() ?   TypeConv<T, int>(int.Parse(s))
                                        : TypeEq<T, long>() ?       TypeConv<T, long>(long.Parse(s))
                                        : TypeEq<T, double>() ?     TypeConv<T, double>(long.Parse(s))
                                        : TypeConv<T, string>(s);
            public static (T,U) Tuple<T,U>() {string[] strs = Strs(); T t = TypeConv<T>(strs[0]); U u = TypeConv<U>(strs[1]); return(t,u);}
            public static (T,U,V) Tuple<T,U,V>() {string[] strs = Strs(); T t = TypeConv<T>(strs[0]); U u = TypeConv<U>(strs[1]); V v = TypeConv<V>(strs[2]); return(t,u,v);}
        }
    }
}