### Problem Statement

An important metric in the theory of sorting is the number of inversions in a sequence. An inversion is any pair of elements that are out of order, meaning that the earlier element in the sequence has a larger value than the later element in the sequence. For example, the sequence

```   3 1 4 2 5
```
has three inversions: 3-1, 3-2, and 4-2.

Given integers n and inv, you are to return a permutation of the sequence 1,...,n that has exactly inv inversions. If it is not possible to create a permutation that has inv inversions, return the empty sequence. If there is more than one permutation that has exactly inv inversions, return the lexicographically earliest. A permutation P is lexicographically earlier than a permutation Q if, at the first index at which the permutations differ, the element in P is smaller than the element in Q.

### Definition

 Class: Inversions Method: createExample Parameters: int, int Returns: int[] Method signature: int[] createExample(int n, int inv) (be sure your method is public)

### Constraints

-n is between 1 and 1000, inclusive.
-inv is between 0 and 1000000, inclusive.

### Examples

0)

 `3` `0`
`Returns: { 1,  2,  3 }`
 The only way for the sequence to have no inversions is for it to be in increasing order.
1)

 `4` `6`
`Returns: { 4,  3,  2,  1 }`
 A sequence in decreasing order.
2)

 `4` `10`
`Returns: { }`
 There is no way to get 10 inversions with only 4 elements.
3)

 `14` `21`
`Returns: { 1,  2,  3,  4,  5,  6,  7,  14,  13,  12,  11,  10,  9,  8 }`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=3492

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=6524&pm=3492

vorthys

#### Testers:

PabloGilberto , lbackstrom

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