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 Problem Statement

Problem Statement for MultiplicationTable3

### Problem Statement

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.

### Definition

 Class: MultiplicationTable3 Method: construct Parameters: int Returns: int[] Method signature: int[] construct(int x) (be sure your method is public)

### Constraints

-x will be between 1 and 1,000, inclusive.

### Examples

0)

 `2`
`Returns: {1, 1, 1, 1 }`
 We have chosen n = 2. Regardless of the inputs, our binary operation \$ always returns 1. For this operation we have exactly x = 2 good subsets of S: the subset {1} and the subset {0,1}.
1)

 `3`
`Returns: {0, 1, 0, 1 }`
 The length of the return value is 4, hence it describes an operation with n = 2. This particular return value describes the following operation: 0 \$ 0 = 0 0 \$ 1 = 1 1 \$ 0 = 0 1 \$ 1 = 1 This operation has exactly 3 good subsets: {0}, {1}, and {0,1}.
2)

 `6`
`Returns: {0, 1, 1, 0, 1, 2, 0, 1, 2 }`
3)

 `31`
`Returns: {0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4 }`
 All non-empty subsets of S are good.
4)

 `1`
`Returns: {0 }`

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This problem was used for:
Single Round Match 689 Round 1 - Division I, Level Two