As the 'Harry Potter' series is over, Harry has no job. As he wants to make quick money, (he wants everything quickly!), he decided to rob banks. He wants to take calculated risks, and grab as much money as possible. But his friends - Hermione and Ron have decided upon a tolerable probability P of getting caught. They feel that it would be safer if he robs a subset of the banks under probablity P.
Input
Input starts with an integer T (≤ 100), denoting the number of test cases.
Each case contains a real number P, the probability as described above, and an integer N (0 < N ≤ 100), the number of banks he is planning to rob.
Then follow N lines, where line j gives an integer Mj (0 < Mj ≤ 100) and a real number pj . Bank j contains Mj million dollars, and the probability of getting caught if he decides to rob bank j is pj. A bank goes bankrupt if it is robbed, and you may assume that all the given probabilities are independent.
Output
For each case, print the case number and the maximum number of millions he can expect to get while the probability of getting caught is less than P.
Sample
| Sample Input | Sample Output |
|---|---|
3 0.04 3 1 0.02 2 0.03 3 0.05 0.06 3 2 0.03 2 0.03 3 0.05 0.10 3 1 0.03 2 0.02 3 0.05 | Case 1: 2 Case 2: 4 Case 3: 6 |
Notes
For the first case, if he wants to rob bank 1 and 2, then the probability of getting caught is 0.02 + (1 - 0.02) * .03 = 0.0494 which is greater than the given probability (0.04). That's why he has only option, just to rob rank 2.