BUD13TLF - Boxes


Given n boxes with widths of w1, w2, . . . , wn and another big box with width W, find how many ways the boxes can be put in the big box. The constrains are:

1) Of course the summation of widths of the placed boxes should not be greater than W.

2) The boxes should be placed one by one starting from left without leaving any empty spaces between them. So, the end of the big box may contain empty spaces. But if there is any unplaced box which can be fit in this space, the ordering should be considered invalid (See the explanation for sample case 1).

3) Two orderings are considered different if in one ordering, one box is in i-th position, but in another ordering, it isn’t.

4) If two boxes have same widths, they should be considered same

Input

Input starts with an integer T (≤ 100), denoting the number of test cases.

Each case starts two integers n (1 ≤ n ≤ 100) and W (1 ≤ W ≤ 1000). The next line contains n space separated integers, denoting w1 w2 . . . wn (1 ≤ wi ≤ W).

Output

For each case, print the case number first and the result modulo 10007.

Example

Input:
2
3 5
1 2 3
5 10
1 2 2 4 5

Output:
Case 1: 6
Case 2: 30

Notes: For the first case of the Sample Input, the orderings are
12
13
21
23
31
32
Only 1 or 2 or 3 is not solutions since we can still place another box.

hide comments
kshubham02: 2017-08-23 07:53:53

Does putting no boxes in the larger box count as an ordering?
Eg, Suppose W=1 and boxes available have widths 2,3, and 4, should the answer be 1?

Alex Anderson: 2015-10-30 07:05:01

Also, I think the cases are too easy relative to the constraints. I think my solution is probably a factor of O(n) too slow, but maybe I optimized enough.

Last edit: 2015-10-30 07:05:11
Alex Anderson: 2015-10-30 06:04:09

Can you fix the way the sample input and output is displayed? It is difficult to read.


Added by:Gầy :))
Date:2015-10-27
Time limit:1s-15s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU JS-MONKEY
Resource:The 2013 ACM-ICPC Asia Phuket Regional Programming Contest