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 Go (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

// ALDS1_4_D - Allocation
// https://onlinejudge.u-aizu.ac.jp/courses/lesson/1/ALDS1/4/ALDS1_4_D

// 最大値の最小値を求める問題。
// 確か最大積載量Pを決め打ちして二分探索するんだった気がする。
// 最大積載量Pは、1 (=重さ1x1個)から、10^9(=重さ10,000 x 100,000個)の範囲の可能性がある。
// 最大積載量Pを1~10^9の間で決め打ちすると、その積載量Pxk台のトラックでn個の荷物を積み切れるか判定するにはO(N)かかる
// 最大積載量Pは2分探索できるので、O(NlogN)で間に合う
func isOK(w []int, p, k int) bool {
	// w: 荷物
	// p: トラック一台あたりの最大積載量
	// k: トラックの台数
	current, tracks := 0, 1
	for i := 0; i < len(w); i++ {
		if current+w[i] <= p {
			current += w[i]
		} else if tracks < k && w[i] <= p {
			current = w[i]
			tracks++
		} else {
			return false
		}
	}
	return true
}
func lbound(w []int, k int) int {
	left, right := 0, 10000*100000
	for right-left > 1 {
		// fmt.Printf("right %d, left %d\n", right, left)
		mid := (left + right) / 2
		if isOK(w, mid, k) {
			right = mid
		} else {
			left = mid
		}
	}
	return right
}
func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	n := nextInt(sc)
	k := nextInt(sc)
	w := make([]int, n)
	for i := range w {
		w[i] = nextInt(sc)
	}
	fmt.Println(lbound(w, k))
}
func nextInt(sc *bufio.Scanner) int {
	sc.Scan()
	t, _ := strconv.Atoi(sc.Text())
	return t
}