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)

def binary_search(arr, max, k)
  left = 0
  right = max
  while left < right do
    mid = (left + right) / 2
    if can_load?(arr.dup, k, mid)
      right = mid
    else
      left = mid + 1
    end
  end
  return left
end

def can_load?(arr,k, p)
  k.times do
    k_load = 0
    while true
      if arr.length == 0
        break
      end

      if k_load + arr[0] <= p
        k_load += arr.shift
      else
        break
      end
    end
  end
  arr.length == 0
end

n, k = gets.split.map(&:to_i)
arr = []
n.times do
  arr << gets.to_i
end
max = 100000 * 10000
ans = binary_search(arr, max, k)
puts ans