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Consider the following series:

A := 1
B := A*2 + 2
C := B*2 + 3 and so on...
Write a program that:

-outputs the number corresponding to a given letter;

-given a string of letters like 'GREP', computes the sum of the numbers corresponding to all the letters in the string (i.e., G + R + E + P), as given by the above series; and

-given a large number (that would fit into a standard 32-bit integer), finds the shortest string of letters corresponding to it. You may use a greedy approach for the last part. Compute the values of the numbers corresponding to letters as and when required and DO NOT pre-compute beforehand and store them in a data structure.

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hello this is
a sample
string to test.