P8960 "WHOI-4" Paper Folding.

Guinness record: a sheet of paper (if nearly $4$ kilometers of toilet paper can be counted as one sheet) can be folded in half at most $13$ times. Little X bragged that he broke this record, but he exaggerated too much.

Little X applied for this record to the Guinness World Records organization, but he happened to be quarantined at home and could not prove it. He had to allow them to ask $t$ questions to confirm that he truly broke the record. For each question, they can ask Little X to fold a sheet of paper in half $n$ times following the rules given by a $01$ string $s$, and then unfold it. For the $i$-th fold, if $s_i = 0$, fold the paper from left to right so that the left side aligns with the right side; if $s_i = 1$, fold the paper from right to left so that the right side aligns with the left side. All folds are made by flipping from the top. **Then it will be unfolded. After unfolding, the paper stays in its original position, only keeping the creases. Check whether you can achieve this.** They want to know whether the $k$-th crease from left to right is an up crease (a crease that protrudes upward) or a down crease (a crease that dents downward). If the answer to the query is an up crease, output `Up`; otherwise output `Down`. Please help the poor Little X. Illustrations of up creases and down creases can be found in the sample explanation.

**This problem uses multiple test cases.** The first line contains a positive integer $t$, the number of test cases. The next $2t$ lines describe the test cases, with each test case taking two lines. For each test case, the first line contains two positive integers $n, k$. The next line contains a $01$ string of length $n$, representing $s$.

Output $t$ lines. Each line contains one string, representing the answer for that test case.

**Sample Explanation** Explanation for Sample #1: Dynamic link: [here](http://img-blog.csdnimg.cn/c68f2ba917504417b109eb1606f4a3a5.gif). For some reason it cannot be displayed on Luogu. Due to technical reasons, the GIF has a relatively low frame rate. For Sample #2, please simulate manually. **Constraints** **This problem uses bundled testdata.** - Subtask 1 ($20$ pts): $t = 10$, $1 \le n \le 5$. - Subtask 2 ($80$ pts): $t = 10^5$. For $100\%$ of the testdata, $1 \le t \le 10^5$, $1 \le n \le 60$, $1 \le k < 2^n$. Translated by ChatGPT 5