Some sequences of bits (3)

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.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:33:55.763Z