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Ex - Multiply or Divide by 2

Score : $600$ points

Problem Statement

You are given multisets with $N$ non-negative integers each: $A=\{ a_1,\ldots,a_N \}$ and $B=\{ b_1,\ldots,b_N \}$.
You can perform the operations below any number of times in any order.

• Choose a non-negative integer $x$ in $A$. Delete one instance of $x$ from $A$ and add one instance of $2x$ instead.
• Choose a non-negative integer $x$ in $A$. Delete one instance of $x$ from $A$ and add one instance of $\left\lfloor \frac{x}{2} \right\rfloor$ instead. ($\lfloor x \rfloor$ is the greatest integer not exceeding $x$.)

Your objective is to make $A$ and $B$ equal (as multisets).
Determine whether it is achievable, and find the minimum number of operations needed to achieve it if it is achievable.

Constraints

• $1 \leq N \leq 10^5$
• $0 \leq a_1 \leq \ldots \leq a_N \leq 10^9$
• $0 \leq b_1 \leq \ldots \leq b_N \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$a_1$ $\ldots$ $a_N$

$b_1$ $\ldots$ $b_N$

Output

If the objective is achievable, print the minimum number of operations needed to achieve it; otherwise, print -1.

3
3 4 5
2 4 6

2

You can achieve the objective in two operations as follows.

• Choose $x=3$ to delete one instance of $x\, (=3)$ from $A$ and add one instance of $2x\, (=6)$ instead. Now we have $A=\{4,5,6\}$.
• Choose $x=5$ to delete one instance of $x\, (=5)$ from $A$ and add one instance of $\left\lfloor \frac{x}{2} \right\rfloor \, (=2)$ instead. Now we have $A=\{2,4,6\}$.

1
0
1

-1

You cannot turn $\{ 0 \}$ into $\{ 1 \} $.