P10836 『FLA - I』Song of Silent River
Background
> You can cry
>
> Drinking your eyes
>
> Do you miss the sadness when it's gone
>
> And you let the river run wild
>
> And you let the river run wild
— _The River_ by _AURORA_
Description
Qiu has two strings $a,b$ of length $n$ that only contain `#` and lowercase letters.
These two strings contain $m$ `#`s in total. Qiu intends to perform $m$ operations to replace all `#`s in the two strings with lowercase letters. For the $i$-th operation, he has to choose a string from $a,b$ and replace the first `#` in this string from left to right with the $(i-1) \bmod 26 +1$-th lowercase letter. **He cannot choose a string that does not contain `#`.**
Qiu has a friend who loves art. He wants to minimize the lexicographic order of the string $a$ after performing $m$ operations. Qiu thought that programming is also a kind of art, and in this way, their hearts will be closer.
Input Format
The first line contains two positive integers $n, m$.
The second line contains a string $a$ of length $n$.
The last line contains a string $b$ of length $n$.
Output Format
Output one line of one string, indicating the minimum $a$ in lexicographic order that can be obtained after executing $m$ operations.
Explanation/Hint
**「Sample Explanation #1」**
In the first operation, Qiu selects the string $a$ and replaces the `#` into $a$ with the $(1-1) \bmod 26+1=1$-st lowercase letter, i.e. `a`; In the second operation, Qiu selects the string $b$ and replaces the `#` in $b$ with the $(2-1) \bmod 26+1=2$-nd lowercase letter, i.e. `b`. The final string $a$ is `thankyou`, which can be proved to be the smallest $a$ in lexicographic order after executing $m$ operations.
**「Constraints」**
|Test Id|$n \leq$|Special Property|
|:-:|:-:|:-:|
|$1 \sim 3$|$10$|No|
|$4 \sim 6$|$10^5$|Yes|
|$7 \sim 10$|$10^5$|No|
- Special Property: It is guaranteed that there is a string in $a,b$ that does not contain `#`.
Each test is worth $10$ points.
For all tests, $1 \leq n \leq 10^5$, $1 \leq m \leq 2n$, the string $a,b$ contains only the character `#` and lowercase letters.