Banana Bunches

Barbara visits Alan's banana farm. The $N$ banana trees stand in one long line, represented by an array $B$. The tree at position $i$ has $B_i$ banana bunches. Every tree costs the same. When Barbara buys a tree, she gets all the banana bunches on it. Alan has a special rule: he does not want too many gaps in his line, so Barbara may buy at most 2 contiguous sections of the tree line. Barbara wants the total number of banana bunches on the trees she buys to equal her basket capacity $K$. She wants to spend as little money as possible. How many trees should she buy?

The first line contains the number of test cases $T$. $T$ test cases follow.

Each test case begins with a line containing two integers $N$, the number of trees on Alan's farm, and $K$, the capacity of Barbara's basket.

The next line contains $N$ non-negative integers $B_1, B_2, \ldots, B_N$, where the $i$-th integer is the number of banana bunches on the $i$-th tree.

For each test case, output one line in the form Case #x: y, where $x$ is the test case number (starting from 1) and $y$ is the minimum number of trees Barbara must buy to get exactly $K$ banana bunches using at most 2 contiguous sections of the farm, or -1 if it is impossible.

• $1 \le T \le 100$.
• $0 \le B_i \le K$, for each $i$ from 1 to $N$.