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Description

ArcSoft, Inc. is a leading global professional computer photography and computer vision technology company.

There are $N$ working blocks in ArcSoft company, which form a straight line. The CEO of ArcSoft thinks that every block should have equal number of employees, so he wants to re-arrange the current blocks into $K$ new blocks by the following two operations:

• merge two neighbor blocks into a new block, and the new block's size is the sum of two old blocks'.
• split one block into two new blocks, and you can assign the size of each block, but the sum should be equal to the old block.

Now the CEO wants to know the minimum operations to re-arrange current blocks into $K$ block with equal size, please help him.

Input

First line contains an integer $T$ ($1\le T\le 100$), which indicates the number of test cases.

Every test case begins with one line which two integers $N$ and $K$ ($1\le N,K\le 10^5$), which is the number of old blocks and new blocks.

The second line contains $N$ numbers $a_1, a_2,\ldots , a_N$ ($1\le a_i\le 10^5$), indicating the size of current blocks.

Output

For every test case, you should output Case #x: y, where x indicates the case number and counts from $1$ and y is the minimum operations.

If the CEO can't re-arrange $K$ new blocks with equal size, y equals $-1$.

Samples

3
1 3
14
3 1
2 3 4
3 6
1 2 3

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

Resources

第二届中国大学生程序设计竞赛 杭州站（CCPC 2016 Hangzhou Site）