Allocation

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.

Constraints

• $1 \leq n \leq 100,000$
• $1 \leq k \leq 100,000$
• $1 \leq w_i \leq 10,000$

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.

Examples

Input

5 3 8 1 7 3 9

Output

10

Input

4 2 1 2 2 6

Output

6

inputFormat

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.

outputFormat

Output

Print the minimum value of $P$ in a line.

Examples

Input

5 3 8 1 7 3 9

Output

10

Input

4 2 1 2 2 6

Output

6

样例

5 3
8
1
7
3
9

10