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 JAVA (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

/**
 * ZAKIREN第5章 4-6.データ構造の応用
 * 
 * @author tdi5277
 *
 */
public class Main {
	/** 入力用 */
	private static BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
	
	/** 出力用 */
	private static StringBuilder stringBuilder = new StringBuilder();
	
	/**
	 * トラックの積載量をチェック。
	 */
	private static int check(int p, int k, int[] w, int n) {
		int i = 0;
		// truckの数だけループ
		for (int j = 0; j < k; j++) {
			// max積載量になるまで
			int internalCapacity = 0;
			while (internalCapacity + w[i] <= p) {
				// 内容量を増やす
				internalCapacity += w[i];
				i++;
				
				// 全ての積載量を積むことができた場合
				if (i == n) {
					return n;
				}
			}
		}
		return i;
	}
	
	/**
	 * メイン。
	 * 
	 * @param args 未使用
	 */
	public static void main(String[] args) {
		try {
			final String SPACE = " ";
			// 読み込み
			String[] temp = bufferedReader.readLine().split(SPACE);
			int n = Integer.parseInt(temp[0]);
			int k = Integer.parseInt(temp[1]);
						
			// n回ループ
			int[] w = new int[n];
			for (int i = 0; i < n; i++) {
				w[i] = Integer.parseInt(bufferedReader.readLine());
			}
			
			// 読み込み終了
			bufferedReader.close();
			bufferedReader = null;
	
			// 二分探索法でPを求める
			int left = 0;
			int right = n * 10000;
			int mid = 0;
			while (right - left > 1) {
				mid = (left + right) / 2;
				// そのPで積み込みきれるかチェック
				int size = check(mid, k, w, n);
				if (size >= n) {
					right = mid;
				} else {
					left = mid;
				}
			}
			stringBuilder.append(right);
			
			// 結果出力
			System.out.println(stringBuilder.toString());
		} catch (Exception e) {
			e.printStackTrace();
		}

	}

}