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.