oql thought of a problem.

Given a sequence $a$ of length $n$. The value of an interval $[l, r]$ is defined as: $$\max(a_l, a_{l+1}, \dots, a_r) \times \min(a_l, a_{l+1}, \dots, a_r) \times (r - l + 1)$$

What is the $k$-th largest interval value?

Input

The first line contains two space-separated integers $n, k$ ($1 \le n \le 5 \times 10^4, 1 \le k \le \frac{n(n + 1)}{2}$), representing the length of the sequence and the query parameter, respectively.

The second line contains $n$ space-separated positive integers, where the $i$-th number represents the value of $a_i$ ($1 \le a_i \le 5 \times 10^4$).

Output

Output a single line containing one positive integer, representing the $k$-th largest interval value.

Examples

Input 1

8 7
1 3 5 6 7 2 4 5

Output 1

70