Problem #125
Happy String
You are given p a's and q b's. You arrange them in the form of a string. If you are able to get a string in which as you move from left to right, the number of a's is strictly greater than b, then it is known as a happy string.
Let the number of such happy strings be denoted by happy(p,q), then find happy(200,100) * 201! * (101!/300!).