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 Scala (judge verdict: Runtime Error)

import scala.io.StdIn.{readInt, readLine};

object Main {
    def main(args: Array[String]): Unit = {
        val Array(n, k) = readLine.split(" ").map(_.toInt);
        val baggage = (0 until n).map(a => readInt).toList;
        println(allocation(baggage, k));
    }
    
    def allocation(baggage: List[Int], k: Int): Int = {
        def binSearch(first: Int, last: Int, min: Int): Int = {
            val pivot = (last + first) / 2;
            if (first == last) {
                if (check(pivot, k, baggage)) pivot else min;
            } else {
                if (check(pivot, k, baggage)) {
                    binSearch(first, pivot - 1, pivot);
                } else {
                    binSearch(pivot + 1, last, min);
                }
            }
        }
        binSearch(1, baggage.sum, Int.MaxValue);
    }
    
    def check(maxCapa: Int, trucks: Int, baggage: List[Int]): Boolean = {
        def go(restCapa: Int, restTrucks: Int, b: List[Int]): Boolean = {
            b match {
                case Nil => true;
                case weight :: restBaggage => {
                    if (weight > maxCapa) {
                        false;
                    } else {
                        if (weight <= restCapa) {
                            go(restCapa - weight, restTrucks, restBaggage);
                        } else {
                            if (restTrucks == 0) {
                                false;
                            } else {
                                go(maxCapa - weight, restTrucks - 1, restBaggage);
                            }
                        }
                    }
                }
            }
        }
        go(0, trucks, baggage);
    }
}