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5 초 512 MB0000.000%

## 문제

Given an rectangular grid of N rows and M columns, each cell can be labeled black (Yin) or white (Yang). Two cells are neighbors if they share a common unit-length edge segment. The grid is valid if all the black cells form a path, and all the white cells form a path. A path is a set S of cells defined as follows:

• The cells form a connected piece. From each cell in S, you can reach any other cell in S by moving between neighbors within S.
• Exactly two cells in S have exactly one neighbor in S each. These are the "ends" of the path.
• Every other cell in S has exactly two neighbors in S.

For example, in the picture below, the first grid is valid, while the second grid is not -- although the black cells form a path, the white cells do not.

Given N and M, compute the number of valid grids. Note that symmetry doesn't matter -- as long as two valid grids differ in one position they are considered different, even if one can be rotated or flipped to the other.

## 입력

The first line of the input will be a single integer T, the number of test cases. T lines follow, each of which contains two integers separated by a space: "N M", as defined above.

### Limits

• 1 ≤ T ≤ 50
• For 80% of the test cases, 4 ≤ NM ≤ 50
• For 90% of the test cases, 4 ≤ NM ≤ 70
• For all test cases, 4 ≤ NM ≤ 100

## 출력

For each test case, output a line in the form "Case #xA", where x is the case number, starting from 1, and A is the number of valid grids of the specified size.

## 예제 입력 1

3
4 4
4 6
5 5


## 예제 출력 1

Case #1: 24
Case #2: 44
Case #3: 48


## 채점 및 기타 정보

• 예제는 채점하지 않는다.