Distribution of independent random variables

Question

I have problem with the following:

We have a random variable $X_1$, which is binomially distributed, i.e. $X_1$ ~ $B_{n,p}$. Furthermore $X_2$ is independent from $X_1$ and is binomially distributed as well, i.e. $X_2$ ~ $B_{m,p}$ with the same probability $p$. What kind of distribution has the following term: $$ X_1 \mid X_1 + X_2$$

Answer 1

$X_1$ is the count of successes among a sequence of $n$ independent Bernoulli trials with identical success rate, $p$.

$X_2$ is the count of successes among a sequence of $m$ independent Bernoulli trials with identical success rate, $p$.

$X_1+X_2$ is ...

So for any given $X_1+X_2$, then $X_1$ is ...