Problem Description

Barbara goes to Alan's banana farm, where the $N$ banana trees are organized in $1$ long line represented by an array $B$. The tree at position $i$ has $B_i$ banana bunches. Each tree has the same cost. Once Barbara buys a tree, she gets all the banana bunches on that tree.

Alan has a special rule: because he does not want too many gaps in his line, he allows Barbara to buy at most $2$ contiguous sections of his banana tree line.

Barbara wants to buy some number of trees such that the total number of banana bunches on these purchased trees equals the capacity $K$ of her basket. She wants to do this while spending as little money as possible. How many trees should she buy?

Input Format

The $1$st line of the input gives the number of test cases, $T$. $T$ test cases follow.

Each test case begins with a line containing $2$ 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 $B_1, B_2, \ldots, B_N$ representing array $B$, where the $i$-th integer represents the number of banana bunches on the $i$-th tree on Alan's farm.

Output Format

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

4
6 8
1 2 3 1 2 3
4 10
6 7 5 2
6 8
3 1 2 1 3 1
4 6
3 1 2 0

Case #1: 3
Case #2: -1
Case #3: 4
Case #4: 3

Hint

In Sample Case #$1$, the first section can contain the trees at indices $2$ and $3$, and the second section can contain the tree at index $6$.

In Sample Case #$2$, it is impossible to achieve a sum of $10$ with $2$ contiguous sections.

In Sample Case #$3$, the first section can contain the trees at indices $\{1, 2\}$, and the second section can contain the trees at indices $\{5, 6\}$. We cannot take the $2 + 3 + 3$ combo (trees at indices $\{1, 3, 5\}$) since that would be $3$ contiguous sections.

In Sample Case #$4$, the only section contains the trees at indices $\{1, 2, 3\}$.

Limits

$1 \le T \le 100$.

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

Test Set $1$

$1 \le K \le 10^4$.

$1 \le N \le 50$.

Test Set $2$

$1 \le K \le 10^4$.

$1 \le N \le 500$.

Test Set $3$

$1 \le K \le 10^6$.

For at most $25$ cases:

$1 \le N \le 5000$.

For the remaining cases:

$1 \le N \le 500$.