Python code for the following:

Your task is to build an array of a specific size by values within the range from lowerbound to upperbound. the array must be strictly increasing at first and then strictly decreasing. If several arrays could be constructed under those constraints, return the winning array with maximum elements starting from the lefthand side. For instance,[3,4,3,2] beats [2,3,4,3], since the first element is larger in the former array. [1,2,3,4,3] beats[1,2,3,2,1], since the fourth element is larger in the former array. If it is impossible to build such an array, return None/null.

Input

The input to the function/method has three arguments:

n, an integer representing the size of the result array; lowerbound an integer representing the lower bound of integer range. The values in result must be more than or equal to lowerbound; upperbound, an integer representing the upper bound of integer range in result. The values in result must be less than or equal to upperbound;

Output

Return a list of integers representing the maximum winning array and if the list is not possible then return None/null.

Constraints

3<=n<=10^6

1<=lowerbound<=upperbound<=10^6

Example

Input:

n=4

lowerbound = 10

upperbound = 12

output:

[11,12,11,10]

Explanation:

In this case, [11,12,11,10] is the winning array. It maintains the constraints of being first strictly increasing and then strictly decreasing, and any other valid arrays, such as [10,11,12,11] and [10,12,11,10] are less than [11,12,11,10]

So [11,12,11,10] is the maximum winning array.

Input:

n=6

lowerbound = 1

upperbound = 3

output:

null

Explanation:

Impossible to construct an array of size n strictly increasing at first and then strictly decreasing within the bounds.