Problem:
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You are given $n$ packages of $w_i$ kg from a belt conveyor in order ($i = 0, 1, ... n-1$). You should load all packages onto $k$ trucks which have the common maximum load $P$. Each truck can load consecutive packages (more than or equals to zero) from the belt conveyor unless the total weights of the packages in the sequence does not exceed the maximum load $P$.

Write a program which reads $n$, $k$ and $w_i$, and reports the minimum value of the maximum load $P$ to load all packages from the belt conveyor.

Input

In the first line, two integers $n$ and $k$ are given separated by a space character. In the following $n$ lines, $w_i$ are given respectively.

Output

Print the minimum value of $P$ in a line.

Constraints

$1 \leq n \leq 100,000$

$1 \leq k \leq 100,000$

$1 \leq w_i \leq 10,000$

Sample Input 1

5 3
8
1
7
3
9

Sample Output 1

10

If the first truck loads two packages of $\{8, 1\}$, the second truck loads two packages of $\{7, 3\}$ and the third truck loads a package of $\{9\}$, then the minimum value of the maximum load $P$ shall be 10.

Sample Input 2

4 2
1
2
2
6

Sample Output 2

6

If the first truck loads three packages of $\{1, 2, 2\}$ and the second truck loads a package of $\{6\}$, then the minimum value of the maximum load $P$ shall be 6.

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ALDS1_4_D
{
    public class Program

    {

        public class LoadCapacityComparer : IComparer<int>
        {
            private int[] items;
            private int k;

            public LoadCapacityComparer(int k, int[] items)
            {
                this.k = k;
                this.items = items;
            }

            public int Compare(int x, int y)
            {
                int sum =0;
                int TruckCount = 1;
                for (int i = 0 ; i < items.Count() ; i++)
                {
                    if (sum + items[i] <= x)
                    {
                        sum += items[i];
                    }
                    else
                    {
                        TruckCount++;
                        if (TruckCount > k) return -1;
                        sum = items[i];                      
                    }
                }
                return 1;   
            }
        }

        public static void Main(string[] args)
        {
            int[] line = ReadIntAr();
            int n = line[0];
            int k = line[1];

            int[] items = new int[n];
            for (int i = 0 ; i < n ; i++) items[i] = ReadInt();

            int itemMax = items.Max();
            int itemSum = items.Sum();

            LoadCapacityComparer lcc = new LoadCapacityComparer(k,items);
            int index = BinarySearch(itemMax,itemSum,lcc);

            Console.WriteLine(~index);

        }

        //●二分探索
        public static int BinarySearch(int left, int right, IComparer<int> comparer)
        {

            int lo = left;
            int hi = right;
            while (lo <= hi)
            {
                int i = GetMedian(lo, hi);
                int c = comparer.Compare(i,0);//yはダミーとして0固定
                if (c == 0) return i;
                if (c < 0) lo = i + 1;
                else hi = i - 1;
            }
            return ~lo;
        }
        private static int GetMedian(int low, int hi) { return low + ((hi - low) >> 1); }

        static string ReadSt() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Console.ReadLine()); }
        static long ReadLong() { return long.Parse(Console.ReadLine()); }
        static double ReadDouble() { return double.Parse(Console.ReadLine()); }
        static string[] ReadStAr(char sep = ' ') { return Console.ReadLine().Split(sep); }
        static int[] ReadIntAr(char sep = ' ') { return Array.ConvertAll(Console.ReadLine().Split(sep), e => int.Parse(e)); }
        static long[] ReadLongAr(char sep = ' ') { return Array.ConvertAll(Console.ReadLine().Split(sep), e => long.Parse(e)); }
        static double[] ReadDoubleAr(char sep = ' ') { return Array.ConvertAll(Console.ReadLine().Split(sep), e => double.Parse(e)); }

    }


}