MultiplicationTable3

Fox Ciel is creating a new binary operation.


The operation will be denoted $ and it will be defined on the finite set S = {0, 1, 2, ..., n-1}. I.e., for each ordered pair (i, j) of elements of S the operation (i $ j) will return some element of S.


For example, we can have S = {0, 1}, and we can define that (0 $ 0) = 0, (0 $ 1) = 1, (1 $ 0) = 0, and (1 $ 1) = 0.


Note that Ciel's operation is not necessarily symmetric. In other words, it is possible that for some i and j the operations (i $ j) and (j $ i) return two different values.


A subset T of S is called good if it has the following property: for any two elements i and j in T, (i $ j) is also in T.


You are given an int x. Construct a binary operation $ with the following properties:

• The number n (i.e., the size of the set S) must be between 1 and 20, inclusive.
• The number of good subsets of the set S must be exactly x.

Return a int[] containing the "multiplication table" of your operation $. More precisely, the return value should consist of n*n elements. For each i and j from the set S, element (i*n+j) of the return value should be the value (i $ j).


If there are multiple solutions, you may return any of them. You may assume that there is always at least one valid solution.