Problem D
24 Game

In his unending goal to become the greatest programmer of all time, Gustav has decided to go to Singapore. Curiosity leads him into the game room, where some of his new friends are playing cards. "What game are you playing?" he asks. His friends go on to tell him about a seemingly ancient mathematical card game called twenty four. The goal is to create the number $T$, typically $24$, using only the numbers on the $C$ cards placed on the table, the four basic arithmetic operators (+,-,*,/) and parentheses. Gustav can also change the order of the cards. Note that unary operators are not allowed (i.e., $1 \cdot -2$ is invalid). Cards with numbers on them take on that value. Ace represents one, Jack represents $11$, Queen represents $12$ and King represents $13$.

Since Gustav’s new friends are incredibly experienced and beat him every single round, help him write a program that can play for him.

Input

The first line contains two positive integers $C$ and $T$ ($1 \le C \le 6$, $1 \le 10^3$), the number of cards and the target number respectively. The second line contains $C$ integers $c_1, c_2, \dots c_ C$ ($1 \le c_ i \le 13$), the cards placed on the table.

Output

Print any solution that equals $T$. There is guaranteed to exist at least one solution.

Points

Your solution will be tested on several test case groups. To get the points for a group, it must pass all the test cases in the group.

4 24
1 12 1 12

(((12-1)+12)+1)

4 24
1 2 3 4

(((4*3)*2)*1)

4 24
3 3 8 8

(8/(3-(8/3)))