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 PHP (judge verdict: Accepted)

<?php

myMain($argv);

class Util
{
    private static $isDebug = false;
    private static $startTime;

    public static function input($isSplitSpace = false)
    {
        $input = trim(fgets(STDIN));
        if (!$isSplitSpace) {
            return $input;
        }

        return explode(' ', $input);
    }

    public static function arrToStr($arr)
    {
        return implode(",", $arr);
    }

    public static function enablingDebug()
    {
        self::$isDebug = true;
        self::$startTime = time();
    }

    public static function DebugLog($text, $isReturn = true)
    {
        if (self::$isDebug) {
            echo $text;
            if ($isReturn) {
                echo PHP_EOL;
            }
        }
    }

    public static function varDump($obj)
    {
        if (self::$isDebug) {
            var_dump($obj);
        }
    }

    public static function arrFirst($arr)
    {
        if (empty($arr) || !is_array($arr)) {
            return null;
        }

        return current($arr);
    }

    public static function printBench()
    {
        if (!self::$isDebug) {
            return;
        }

        echo sprintf(" Time: %.3f s" . PHP_EOL, time() - self::$startTime);
    }
}

function myMain($argv)
{
    if (!empty($argv[1])) {
        Util::enablingDebug();
    }

    // START
    list($n, $leastTrack) = Util::input(true);
    $bList = [];
    for ($i = 0; $i < $n; ++$i) {
        $bList[] = Util::input();
    }

    $left = max($bList);
    $right = array_sum($bList);
    while ($right - $left > 1) {
        $mid = floor(($left + $right) / 2);
        if (isOkP($mid, $leastTrack, $bList)) {
            $right = $mid;
        } else {
            $left = $mid;
        }
        Util::DebugLog($left . "   " . $right);
    }

    if (isOkP($left, $leastTrack, $bList)) {
        echo $left . PHP_EOL;
    } else {
        echo $right . PHP_EOL;
    }

    // bench
    Util::printBench();
}

// 1. 荷物をトラックに運び入れる
// 2. トラックに詰めなかった場合は
//   2-1. 次のトラックがある場合は、今のトラックを出発させ、次のトラックを呼ぶ
//   2-2. 次のトラックがない場合は、チャレンジ失敗
function isOkP($p, $leastTrack, $bList)
{
    $leastP = $p;
    foreach ($bList as $b) {
//        Util::DebugLog(sprintf("  b: %d, leastP: %d, track: %d  ", $b, $leastP, $leastTrack), 0);
//        Util::DebugLog("  b: " . $b, 0);
        // 1
        if ($leastP >= $b) {
            $leastP -= $b;
//            Util::DebugLog(sprintf("  leastP: %d ", $leastP));
            continue;
        }

        // 2
        if ($leastTrack > 1) {
            // 2-1
            $leastTrack -= 1;
            $leastP = $p - $b;
//            Util::DebugLog(sprintf("  leastP: %d, track: %d  ", $leastP, $leastTrack));
            continue;
        }

        // 2-2
        return false;
    }

    return true;
}