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: Accepted)

#方針
# 最大積載量pのとき、k台のトラックでどこまで積めるか探索していく
#二分探索していく。rightの初期値は10,000*100,000
# あるpを選んだときに、k台のトラックで積める個数がnよりも大きかったら探索テーブルの左
# あるpを選んだときに、k台のトラックで積める個数がnよりも小さかったら探索テーブルの右

$n, $k = gets.split.map(&:to_i)
$w = Array.new($n){gets.to_i}

#最大積載量pのとき、k台のトラックで何個の荷物を積めるか返す関数
def f(p)
  cur = 0 #積荷の何個目を積み込もうとしているか
  truck = Array.new($k){p} #各トラックにあと何キロ積めるか

  truck.each_with_index do |t, i|
    while $w[cur] && truck[i] - $w[cur] >= 0
      truck[i] = truck[i] - $w[cur]
      cur += 1
    end
  end
  return cur
end


def binary_search()
  left = 0
  right = 100000*10000
  while (right-1 > left)
    mid = (left+right)/2
    tmp = f(mid)
    if tmp >= $n
      right = mid
    else
      left = mid
    end
  end
  return right
end

p binary_search