The economically questionable lottery business is making a mass-produced rectangular scratch card. It consists of a grid of hidden upper-case letters; you win by scratching letters so that they form a certain phrase, also consisting of upper-case letters. It might look like this one, where you would like to find the phrase “DWITEISAWESOMEHAHA”:

DLFKJW FKIGDT EKIKSA WQEDSO MEHAHA

You would like to mass-produce correctly scratched scratch cards to sell in the black market. To do this, you would like to have a stencil of the same size as the grid. For example, using this stencil, where “.” means “scratch” and “#” means “don’t scratch”:

.####. ##.##. .#.#.. .#.#.. ......

You obtain the correct solution:

D####W ##I##T E#I#SA W#E#SO MEHAHA

Given a grid of letters and a phrase, you would like to construct a stencil to solve this puzzle. If in fact there is no solution, you should output a stencil with the letter “x” for each spot.

The input file **DATA2.txt** will contain 5 test cases. Each test case will begin with a line of two space-separated integers 1 ≤ `H`, `W` ≤ 10, the height and width of the grid. The next `H` lines will contain `W` upper-case letters each, describing the grid of letters. The final line of each test case will be a single string of upper-case letters, the solution string.

The output file **OUT2.txt** will contain 5 sets of stencils, as described above. You may assume that solutions are unique. Refer to the sample output’s format.

```
5 6
DLFKJW
FKIGDT
EKIKSA
WQEDSO
MEHAHA
DWITEISAWESOMEHAHA
2 2
AB
CD
E
```

```
.####.
##.##.
.#.#..
.#.#..
......
xx
xx
```