Ex - Multiply or Divide by 2

AtCoder

IDabc254_h

Time2500ms

Memory256MB

Difficulty—

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: $N$ $a_1$ $\ldots$ $a_N$ $b_1$ $\ldots$ $b_N$ [samples]

Samples

Input #1

3
3 4 5
2 4 6

Output #1

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 $A={2,4,6}$.

Input #2

1
0
1

Output #2

\-1

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

API Response (JSON)

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