XOR pairs

For given non-negative integers $X$, $A$, and $B$, consider all pairs of non-negative integers $(a,b)$ such that a\ \mathrm{xor}\ b = X, a \geq A, and b \geq B. Here, $a\mathrm{xor}b$ denotes the bitwise XOR operation ("$\text{xor}$" in Pascal, "\textbf{\^{}}" in C/C++/Java). Sort these pairs in increasing order by $a$, and for pairs with the same $a$, in increasing order by $b$.

You need to find the $N$-th pair among these pairs. Numbering starts from $1$. You will need to answer thousands of such queries for the given $X$, $A$, $B$.