Series Generation Challenge

In this problem, you are required to generate a numerical series based on a specified pattern. Four patterns are supported:

1. Arithmetic: The series starts at a specified number and increments by 1 for each subsequent element. Mathematically, the nth term is given by (a_n = a_0 + n), where (a_0) is the starting number.

2. Fibonacci: The series begins with the given starting number and the next consecutive number. Every subsequent element is the sum of the previous two. That is, (a_0 = \text{start}), (a_1 = \text{start}+1) and (a_n = a_{n-1} + a_{n-2}) for (n \ge 2).

3. Geometric: The series starts from the initial number and each next element is twice the previous one. In formula, (a_n = a_0 \times 2^n).

4. Square: The series consists of squares of consecutive numbers starting from the given number. That is, (a_n = (\text{start}+n)^2).

Your program should read the input from stdin, generate the corresponding series based on the provided pattern, and output the series to stdout as space-separated integers.

inputFormat

The input is provided as a single line containing three items separated by spaces:

• An integer length (the number of elements in the series).
• An integer start (the starting number of the series).
• A string pattern which will be one of: "arithmetic", "fibonacci", "geometric", or "square".

Example: 5 2 arithmetic

outputFormat

Output the generated series as a single line of space-separated integers. If the length is 0 or negative, output an empty line.## sample

5 2 arithmetic

2 3 4 5 6