Cut Tiles (Small)

Enzo is renovating the house he just bought. The hardest part is buying exactly the right number of tiles.

Enzo needs $N$ square tiles, and the side length of the $k$-th tile is $2^{S_k}$. The store sells only square tiles of size $M \times M$. Enzo cuts the tiles he buys along lines parallel to their sides, and every tile he needs is cut out of them. Each required tile must be cut whole out of a single purchased tile, and separate pieces cannot be joined together.

What is the smallest number of tiles Enzo has to buy?

The first line contains the number of test cases $T$. Each of the next $T$ lines holds one test case. A line starts with the number of required tiles $N$ and the size $M$ of the tiles the store sells, followed by the $N$ integers $S_1, S_2, \dots, S_N$ that fix the sizes of the required tiles.

Limits

• $1 \le T \le 100$
• $1 \le N \le 20$
• $1 \le 2^{S_k} \le M \le 2^{31}-1$

For each test case, print one line in the form "Case #x: y", where $x$ is the test case number starting from 1 and $y$ is the smallest number of tiles Enzo has to buy.