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 Rust (judge verdict: Accepted)

use std::io;

fn main() {
    let nk = read_vec::<usize>();
    let n = nk[0];
    let k = nk[1];
    let mut w = Vec::new();

    for _ in 0..n {
        w.push(read::<i32>());
    }
    println!("{}", search(&w, k as i32));
}

// 2分探索 O(logn)
// ソート済みのデータを入力
pub fn search(a: &[i32], key: i32) -> i32 {
    // 最大積載量Pの最小値は最大荷物の重さ
    let mut min = *a.clone().into_iter().max().unwrap();
    let mut max = a.clone().iter().sum::<i32>();
    let mut ans = max;

    while min < max {
        let mid: i32 = (min + max) / 2;
        let p = need_track(&a, &mid);
        if p > key {
            min = mid + 1;
        } else {
            max = mid;
            ans = if min > max { min } else { max };
        }
    }
    ans
}

// 何台のトラックが必要か数える
fn need_track(a: &[i32], p: &i32) -> i32 {
    let mut count = 1;
    let mut shipment= 0;
    for &num in a {
        shipment += num;
        if shipment > *p {
            count += 1;
            shipment = num;
        }
    }
    count
}

/// 標準入力から一行を読み取り、空白文字で分割し、各要素を指定の型に変換する関数
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut line = String::new();
    io::stdin().read_line(&mut line)
        .ok()
        .expect("Faild to read Vec");
    line.trim().split_whitespace()
        .map(|i| i.parse().ok().unwrap()).collect()
}

/// 標準入力から一行を読み取り、指定の型に変換する関数
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}