K-th Largest Subarray Sum

Given an array with $n$ elements, what is the $k$-th largest sub array sum. (A subarray sum is the sum of all elements within a continuous section of the array).

Input

The first line contain integers $n$ and $k$. The second line contains $n$ integers $a_1,\dots,a_n$, the elements of the array.

Output

Output the $k$-th largest subarray sum.

Constraints

• $1 \le n \le 10^4$
• $1 \le k \le \frac{n(n+1)}{2}$
• $1 \le a_i \le 10^9$

Example 1

10 1
7 7 4 6 3 8 9 8 5 1 

58

Example 2

3 4
8 10 4 

10

Example 3

5 6
3 6 9 8 4 

18