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.util.Scanner;

public class Main {

    static Scanner scan;
    static int[] W;
    static final int n = 0;
    static final int k = 0;

    public static void main(String[] args) {
        scan = new Scanner(System.in);

        int n = scan.nextInt();
        int k = scan.nextInt();
        int gross = 0;
        W = new int[n];

        for(int i = 0; i < n; i++) {
            W[i] = scan.nextInt();
            gross += W[i];
        }

        if(k == 1) {
            System.out.println(gross);
            return ;
        }
        int min = gross / k; // 積載重量平均値
        int max = gross; // 合計積載重量最大値
        int mid = (max + min) / 2;

        while(max - min > 1) {
            mid = (max + min)/2;
            if(carry(mid, k, n)) {
                max = mid;
                continue;
            } else break;
        }

        while(true) {
            if(carry(max, k, n)) {
                max--;
                continue;
            }
            else {
                max++;
                break;
            }
        }
        System.out.println(max);
    }

    static public boolean carry(int P, int k, int n) {
        if(P == 0) {
            return false;
        }
        int j = 0;
        for(int i = 0; i < k; i++) {
            int s = 0;
            while(s + W[j] <= P) {
                s += W[j];
                j++;
                if(j == n) return true;
            }
        }
        return false;
    }
}