Binary Table

Kipa received an $n$ by $n$ table filled with 0s and 1s as a gift from Yul. Kipa liked the gift so much that Kipa wrote, to the right of each row, the value of that row read as a binary number and converted to decimal. In the same way, Kipa wrote below each column the value of that column read as a binary number, and wrote the sum of all those values in the bottom-right corner.

Then Minti took the table. Minti told Kipa the $(n+1)$ numbers in the rightmost column, in shuffled order, and then burned Kipa's precious table!

Kipa worked out which of the numbers Minti gave is $X$, the one in the bottom-right corner. But Kipa is too sad to continue. Can you do this for Kipa?

The first line contains a positive integer $n$ at most $10^3$ and a positive integer $X$ less than $10^{320}$.

From the second line, $n$ lines follow. Each contains one of the $(n+1)$ numbers Minti gave, excluding $X$. Each number is a positive integer, the numbers are distinct, and each is less than $2n$.

All numbers are given in decimal.

If the given information determines the table uniquely, print the original $n$ by $n$ table without spaces. Otherwise, print kipa so sad :(.

For the first input, the table below can be built, and it is unique.