Some sequences of bits (3) P59506

Write a program that prints the number of sequences made up of exactly $z$ zeros and $u$ ones that are multiple of three when considered as a binary number. Note that numbers that begin with one or more zeros are allowed here.

For instance, there are 9 sequences for $z = 2$ and $u = 4$: $$001111 \quad 011011 \quad 011110 \quad 100111 \quad 101101 \quad 110011 \quad 110110 \quad 111001 \quad 111100$$

Input

Input consists of several pairs of natural numbers $z$ and $u$, each between 0 and 30.

Output

For every pair of $z$ and $u$, print the required number.