시간 제한메모리 제한제출정답맞힌 사람정답 비율
5 초 512 MB27252090.909%

## 문제

The Lottery is changing! The Lottery used to have a machine to generate a random winning number. But due to cheating problems, the Lottery has decided to add another machine. The new winning number will be the result of the bitwise-AND operation between the two random numbers generated by the two machines.

To find the bitwise-AND of X and Y, write them both in binary; then a bit in the result in binary has a 1 if the corresponding bits of X and Y were both 1, and a 0 otherwise. In most programming languages, the bitwise-AND of X and Y is written X&Y.

For example:
The old machine generates the number 7 = 0111.
The new machine generates the number 11 = 1011.
The winning number will be (7 AND 11) = (0111 AND 1011) = 0011 = 3.

With this measure, the Lottery expects to reduce the cases of fraudulent claims, but unfortunately an employee from the Lottery company has leaked the following information: the old machine will always generate a non-negative integer less than A and the new one will always generate a non-negative integer less than B.

Catalina wants to win this lottery and to give it a try she decided to buy all non-negative integers less than K.

Given A, B and K, Catalina would like to know in how many different ways the machines can generate a pair of numbers that will make her a winner.

Could you help her?

## 입력

The first line of the input gives the number of test cases, T. T lines follow, each line with three numbers A B K.

Limits

• 1 ≤ T ≤ 100.
• 1 ≤ A ≤ 1000.
• 1 ≤ B ≤ 1000.
• 1 ≤ K ≤ 1000.

## 출력

For each test case, output one line containing "Case #x: y", where x is the test case number (starting from 1) and y is the number of possible pairs that the machines can generate to make Catalina a winner.

## 예제 입력 1

5
3 4 2
4 5 2
7 8 5
45 56 35
103 143 88



## 예제 출력 1

Case #1: 10
Case #2: 16
Case #3: 52
Case #4: 2411
Case #5: 14377


## 힌트

In the first test case, these are the 10 possible pairs generated by the old and new machine respectively that will make her a winner: <0,0>, <0,1>, <0,2>, <0,3>, <1,0>, <1,1>, <1,2>, <1,3>, <2,0> and <2,1>. Notice that <0,1> is not the same as <1,0>. Also, although the pair <2, 2> could be generated by the machines it wouldn't make Catalina win since (2 AND 2) = 2 and she only bought the numbers 0 and 1.

## 채점 및 기타 정보

• 예제는 채점하지 않는다.