## Goal

It is a well known fact that ants always move in a straight line. However, not many people know what happens when two groups of ants meet face to face in a passage which is too narrow for any two ants to evade laterally each other. One theory suggests that they start jumping over each other.

From the moment the groups meet, every second, ants which are facing an ant moving in opposite direction jump (or gets jumped over, depending on the deal they made) over it.

For example, given two groups, say ABC and DEF.

When they meet it's like this: CBADEF

Since they can't bypass each other, they start jumping:

After 1 second, it becomes CBDAEF

After 2 seconds, it becomes CDBEAF

After 3 seconds, it becomes DCEBFA

After 4 seconds, it becomes DECFBA

And finally, it becomes DEFCBA

From this point on, groups have jumped over each other and any seconds after this, the state remains the same.

Your job is to determine the order of ants in the passage after T seconds.
Input

**Line 1:** Two integers `N1` and `N2`, lengths of two groups.

**Line 2:** String `S1`, first group of ants.

**Line 3:** String `S2`, second group of ants.

**line 4:** An integer `T`, the number of seconds passed.

Output

**Single line:** Containing the state of groups after `T` seconds

Constraints

0 < `N1`, `N2` < 50

0 ≤ `T` < 50