Jumpers

A cyclic tape has $n$ cells. Some are painted black and some white. Your task is to paint every cell black. To paint them you use jumpers: hopping robots dipped in black paint. When a jumper lands on a white cell, it repaints that cell black. A jumper may never land on a black cell. You may use any number of jumpers, and for each jumper you pick any white cell as its start; the chosen starting cells must be pairwise distinct.

Every jumper must make at least one jump and finish back on the cell it started from. A jumper paints its own starting cell only on its final jump. All jumpers are identical: they share one set of possible jumps $S = \{s_1, \dots, s_m\}$. From its current cell a jumper may perform any one of the $m$ moves, as long as that jump obeys the rules above. The $i$-th move sends the jumper $s_i$ cells clockwise.

For a given tape and jumper specification, decide whether it is possible to repaint the whole tape black while respecting all of the rules above.

The first line contains an integer $t$ ($1 \le t \le 20$), the number of test sets. The test sets follow.

Each test set begins with a line holding two integers $n$ and $m$ ($1 \le n \le 500$, $1 \le m \le n$): $n$ is the tape length and $m$ is the number of possible jump lengths. The next line is a string of $n$ characters B and C describing the cyclic tape (B is a white cell, C is a black cell). Each of the following $m$ lines holds one integer $s_i$ ($1 \le s_i \le n$), one of the jumper's possible jump lengths.

For each test set output one line with a single word: TAK if the tape can be painted entirely black, or NIE otherwise.