Meera bought a house on Mars, and plans to decorate it with chains of alien flowers. Each flower is either red () or blue (), and Meera knows how many occurrences of RR, RB, BB, and BR she wants to see in a chain.

The diagram below shows a flower chain of length :

In this example, RR occurs times (at positions and ), RB occurs times (at positions , , and ), BB occurs time (at position ), and BR occurs times (at positions , , and ).

Meera wants your help determining how many different chains with positive length can be made. Given , and , find the number of different chains having occurrences of RR, RB, BB and BR equal to inputs , and , respectively. As the answer can be very large, your printed output should be .