### Problem Statement

Given a number N and a length L, find the shortest list of at least L consecutive non-negative integers whose sum is N. If the length of that list is 100 or smaller, return the sequence as a int[] in ascending order. If there is no such sequence or its length is larger than 100, return { }.

### Definition

 Class: SequenceSums Method: sequence Parameters: int, int Returns: int[] Method signature: int[] sequence(int N, int L) (be sure your method is public)

### Constraints

-N will be between 1 and 1000000000, inclusive.
-L will be between 2 and 100, inclusive.

### Examples

0)

 `18` `2`
`Returns: {5, 6, 7 }`
 18 can be expressed as 5 + 6 + 7 or 3 + 4 + 5 + 6. Both of these lists contain more than 2 elements, so you should return the shortest among them.
1)

 `18` `4`
`Returns: {3, 4, 5, 6 }`
 Now the correct answer is 3 + 4 + 5 + 6 because 5 + 6 + 7 contains less than 4 elements.
2)

 `18` `5`
`Returns: { }`
 Both possible presentations of 18 contain less than 5 elements, so there's no answer for this case.
3)

 `45` `10`
`Returns: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }`
4)

 `1000000000` `2`
`Returns: {199999998, 199999999, 200000000, 200000001, 200000002 }`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10241

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=13759&pm=10241

legakis

#### Testers:

PabloGilberto , Jan_Kuipers , ivan_metelsky

#### Problem categories:

Math, Simple Search, Iteration