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: Wrong Answer)

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

namespace myApp
{
    class Program
    {
        // 制約
        const int MAX = 100000;

        // 荷物の重さ
        static int[] baggageWeight = new int[MAX];

        static int baggageCount = 0;
        static int truckCount = 0;

        // 最大積載量Pのk台のトラックで何個の荷物を積めるか
        static int Check(int P) {
            int count = 0;
            for (int i = 0; i < truckCount; i++) {
                int s = 0;
                while (s + baggageWeight[count] <= P) {
                    s += baggageWeight[count];
                    count++;
                    if (count == baggageCount) { return baggageCount; }
                }
            }

            // すべての荷物を積めてない
            return count;
        }

        // 二分探索
        static int Solve() {
            int left = 0;
            // 最大積載量Pの最大値は最大の荷物の個数×1個あたりの最大重量
            int right = 10000 * 10000;

            while (right - left > 1) {
                var mid = (left + right) / 2;
                int v = Check(mid);
                if (v >= baggageCount) {
                    // 荷物を積めることができた最大積載量Pをrightに入れる
                    right = mid;
                } else {
                    // baggageCOunt未満は荷物を積めなかった
                    left = mid;
                }
            }

            return right;
        }

        static void Main(string[] args)
        {
            // 入力
            var line = Console.ReadLine().Split(' ');
            baggageCount = int.Parse(line[0]);
            truckCount = int.Parse(line[1]);
            for (int i = 0; i < baggageCount; i++) {
                baggageWeight[i] = int.Parse(Console.ReadLine());
            }

            // 処理
            var ans = Solve();

            // 出力
            Console.WriteLine(ans);
        }
    }
}