A Mystery Algorithm on Nondeterministic finite automata

Consider the Mystery Algorithm below:

Input: NDFAs $M_1 = (Q_1,\Sigma_1,\Delta_1,s_1,W_1)$ and $M_2 = (Q_2,\Sigma_2,\Delta_2,s_2,W_2)$, where $Q_1 \cap Q_2 = \emptyset$

Output: NDFA M such that _______________________ ←it's a mystery!

$M = (Q_1 \cup Q_2 \cup \{s\}, \Sigma_1 \cup \Sigma_2, \Delta_1 \cup \Delta_2 \cup \{(s,\lambda,s_1),(s,\lambda,s_2)\}, s, W_1 \cup W_2)$,

where s ∉ Q1 and s ∉ Q2 (i.e. s is a new state)

Here are a couple of questions to answer about this mystery algorithm:

1. What 5-tuple does this algorithm produce for the input machines given below?

   M1 = ({p0,p1}, {a,b}, {(p0,a,p1),(p1,a,p0)}, p0, {p1}) and M2 = ({q0,q1}, {a,b}, {(q0,b,q1),(q1,b,q0)}, q0, {q0})
2. Draw the diagram for your answer to part 1.
3. Give a concise english description of what the Mystery Algorithm accomplishes in general (i.e. for any two input machines). In other words, fill in the blank in the output specification above.