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 Ruby (judge verdict: Wrong Answer)

#!/usr/bin/ruby
# -*- coding: utf-8 -*-
=begin
ALDS1_4-D
=end

class Main
  def sum(f)
    f.inject(0){|acc,x| acc + x}
  end

  def ndivide(f,x,i)
    n=f.length
    return nil if f.max > x
    m=0
    i=0
    while i <= n-1 do
      m += 1
      if m > i then 
        return nil
      end
      j = i
      while j <= n-1 do
        if sum(f.slice(i..j)) > x then
          j -= 1
          break
        end
        j += 1
      end
      i=j+1
    end
    m
  end
# 227994
  def initialize
    #fh=open("ALDS1_4_Din.txt")
    #fh=open("/home/muz/Downloads/ALDS1_4_D_in23.txt")
    #fh=open("/home/muz/Downloads/ALDS1_4_D_in25.txt")
    #fh=open("/home/muz/Downloads/ALDS1_4_D_in28.txt")
    #fh=open("/home/muz/Downloads/ALDS1_4_D_in35.txt")
    fh=STDIN
    f=[]
    n,m=fh.gets.chomp.split.map{|x| x.to_i}

    0.upto(n-1){|i|
      f.push(fh.gets.to_i)
    }

    total = sum(f)
    st = f.max
    ans=0

    x0 = st
    x1 = total
    while true do
      x2 = (x0 + x1)/2
      #puts "#{x0} #{x2} #{x1} "
      q=ndivide(f,x2,m)
      if  q and q <= m then
          x1 = x2
      else
        x0 = x2
      end
      if  x0+1==x1 then
        ans=x0
        break
      end
    end
    puts ans

  end
end

if $0==__FILE__ then
  Main.new()
end