Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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::collections::VecDeque;
use std::env;
//use std::fmt::Debug;
use std::io;
use std::io::prelude::*;
//use std::time::{Duration, Instant};

//===================================================
// MACROs need to be defined above the use place ... ?
macro_rules! dprintln {
    ($($x:expr),*) => {{
        if $crate::is_debug_mode() {
            let f = || {println!( $($x),*)};
            f()
        }
    }}
}

/// Backward For-Loop Helper
///  from -> to (exclude `to`)
///
/// # Examples
/// see tests::macro_backward()
///
#[macro_export]
macro_rules! backward_ho {
    ($from:expr, $to:expr) => {{
        (($to + 1)..($from + 1)).rev()
    }};
}
//===================================================

fn main() {
    // Initialize
    set_debug_mode(false);
    for arg in env::args() {
        if arg == "--debug" {
            set_debug_mode(true);
        }
    }
    dprintln!("[DebugMode] {}", "On");

    // Execute
    dprintln!("=================");
    dprintln!("= READ INPUT     ");
    let stdin = io::stdin();
    let input = BufReadInput::new(stdin.lock());
    dprintln!("[Input] \n{:?}", input);
    dprintln!("=================");
    dprintln!("= INTERPRET INPUT");
    let q = input.into_quiz();
    dprintln!("[Quiz] \n{:?}", q);
    dprintln!("=================");
    dprintln!("= SOLVE QUIZE    ");
    let a = q.solve();
    dprintln!("[Answer] \n{:?}", a);
    dprintln!("=================");
    dprintln!("= PRINT ANSWER   ");
    a.print();
    dprintln!("=================");
}

#[derive(Debug)]
struct Quiz {
    n: usize,    // 1 <= n <= 100,000
    k: usize,    // 1 <= k <= 100,000
    w: Vec<u32>, // 1 <= w[i] <= 10,000, length=n
}

#[derive(Debug)]
struct Answer {
    min_p: u32,
}

trait IntoQuiz {
    fn into_quiz(self) -> Quiz;
}

impl<I: Input> IntoQuiz for I {
    fn into_quiz(mut self) -> Quiz {
        let n: usize = self.parse_next().unwrap();
        let k: usize = self.parse_next().unwrap();
        let w: Vec<u32> = self.parse_next_vec(n).unwrap();
        Quiz { n, k, w }
    }
}

impl Quiz {
    fn solve(self) -> Answer {
        let mut left_c_p = 1;
        let mut right_o_p = (10_000 * self.n as u32) / self.k as u32 + 1; // when max(w_i)=10,000

        while left_c_p < right_o_p {
            let mid_p = (right_o_p + left_c_p) / 2;
            dprintln!("search {} - {} - {}", left_c_p, mid_p, right_o_p);

            if Quiz::check(mid_p, self.k, &self.w) {
                // search left
                dprintln!(" {} is ok. next search left.", mid_p);
                right_o_p = mid_p;
            } else {
                // search right
                dprintln!(" {} is ng. next search right.", mid_p);
                left_c_p = mid_p + 1;
            }
        }

        Answer{ min_p : right_o_p }
    }

    fn check(p: u32, k: usize, w: &Vec<u32>) -> bool {
        // greedy 
        let mut r_p = p;
        let mut r_k = k;

        for &wi in w {
           if wi <= r_p {
               // Current truck can take w[i]
               r_p -= wi;
           } else {
               // Consider next truck
               if r_k > 1 && wi <= p {
                   // Next truck can take w[i]
                   r_k -= 1;
                   r_p = p - wi;
               } else {
                   // There is no truck can take wi.
                   return false;
               }
           }
        }
        true
    }
}

impl Answer {
    fn print(self) {
        println!("{}", self.min_p);
    }
}

// =====================================================
// =
// =====================================================

//==================================================
// Stdin Reader
#[derive(Debug)]
pub enum Token {
    Word(String),
    LineBreak,
}

impl Token {
    pub fn is_word(&self) -> bool {
        match *self {
            Token::Word(ref _x) => true,
            _ => false,
        }
    }
}

#[derive(Debug)]
pub struct BufReadInput<R: BufRead> {
    input: R,
    tokens: VecDeque<Token>,
}

pub trait Input {
    fn read_next_word(&mut self) -> Option<Token>;

    fn parse_next<T>(&mut self) -> Option<T>
    where
        T: std::str::FromStr,
    {
        if let Some(Token::Word(str)) = self.read_next_word() {
            match str.parse() {
                Ok(x) => Some(x),
                _ => None,
            }
        } else {
            None
        }
    }

    fn parse_next_vec<T>(&mut self, size: usize) -> Option<Vec<T>>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::new();

        for _i in 0..size {
            if let Some(t) = self.parse_next() {
                v.push(t);
            } else {
                return None;
            }
        }

        Some(v)
    }

    fn parse_next_vec2<T>(&mut self, size2: usize, size1: usize) -> Option<Vec<Vec<T>>>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::new();

        for _i in 0..size2 {
            if let Some(t) = self.parse_next_vec(size1) {
                v.push(t);
            } else {
                return None;
            }
        }

        Some(v)
    }

    fn parse_all_remaining_into_vec<T>(&mut self) -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::new();

        loop {
            match self.parse_next() {
                Some(x) => v.push(x),
                None => return v,
            }
        }
    }
}
impl<R: BufRead> BufReadInput<R> {
    pub fn new(input: R) -> Self {
        let tokens = VecDeque::new();

        BufReadInput { input, tokens }
    }
}

impl<R: BufRead> Input for BufReadInput<R> {
    fn read_next_word(&mut self) -> Option<Token> {
        loop {
            match self.tokens.pop_front() {
                None => {
                    // Read Input
                    let mut line = String::new();
                    let n = self.input.read_line(&mut line).expect("Read Error.");
                    if n == 0 {
                        return None;
                    }
                    let mut line_tokens = tokenaize(line);
                    self.tokens.append(&mut line_tokens);
                }
                Some(Token::LineBreak) => (),
                x => return x,
            }
        }
    }

}

//TODO: Make CaseIterator
// ex) 
//  let mut input: Input ...
//  let mut iter: CaseIterator<Case=Command> = input.rest_into_cases(|i|   
//    let cmd:String = i.parse_next().expect("Parse error cmd");
//    let num:u32    = i.parse_next().expect("Parse error num");
//
//    Command::new(cmd, num)
//  );
//  let case1 = iter.next();
//  let case2 = iter.next();
//  ...


fn tokenaize(str: String) -> VecDeque<Token> {
    let mut v = VecDeque::new();

    for w in str.split_whitespace() {
        v.push_back(Token::Word(w.to_string()));
    }
    v.push_back(Token::LineBreak);
    v
}

//==================================================
// Utility Functions
pub fn concat_vec_to_string<T>(v: &Vec<T>) -> String
where
    T: std::fmt::Display,
{
    let mut string = String::with_capacity(v.len() * 2);

    if let Some((h, t)) = v.split_first() {
        string = h.to_string();

        for obj in t {
            string.push(' ');
            string.push_str(&obj.to_string());
        }
    }

    return string;
}

//==================================================
// Debug Switch
static mut S_DEBUG_MODE: bool = false;
fn is_debug_mode() -> bool {
    unsafe { S_DEBUG_MODE }
}

fn set_debug_mode(mode: bool) {
    unsafe {
        S_DEBUG_MODE = mode;
    }
}

//==================================================
// Usage
#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn macro_backward() {
        let mut v = Vec::new();
        for i in backward_ho!(5, 1) {
            v.push(i);
        }
        assert_eq!(vec![5, 4, 3, 2], v);
    }
}