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.

8 2
th#nkyou
#estwish

thankyou

16 5
##soluteradian#e
your#awnwillcom#

absoluteradiance

40 45
hhuj#pzr#k#mmd#z##y#o####m##j##tga#k#t#g
m########be#######vf##a#j###ypuf###pr###

hhujapzrakbmmdczdeyfoghijmkljmntgaokptqg

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」

• 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.