Pairs

We have N integers A_1, A_2, ..., A_N.

There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?

Constraints

• All values in input are integers.
• 2 \leq N \leq 2 \times 10^5
• 1 \leq K \leq \frac{N(N-1)}{2}
• -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N K A_1 A_2 \dots A_N

Output

Print the answer.

Examples

Input

4 3 3 3 -4 -2

Output

-6

Input

10 40 5 4 3 2 -1 0 0 0 0 0

Output

6

Input

30 413 -170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0

Output

448283280358331064

inputFormat

input are integers.

• 2 \leq N \leq 2 \times 10^5
• 1 \leq K \leq \frac{N(N-1)}{2}
• -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N K A_1 A_2 \dots A_N

outputFormat

Output

Print the answer.

Examples

Input

4 3 3 3 -4 -2

Output

-6

Input

10 40 5 4 3 2 -1 0 0 0 0 0

Output

6

Input

30 413 -170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0

Output

448283280358331064

样例

10 40
5 4 3 2 -1 0 0 0 0 0

6