Time Limit: 2 second(s) | Memory Limit: 32 MB |
Factorial of an integer is defined by the following function
f(0) = 1
f(n) = f(n - 1) * n, if(n > 0)
So, factorial of 5 is 120. But in different bases, the factorial may be different. For example, factorial of 5 in base 8 is 170.
In this problem, you have to find the number of digit(s) of the factorial of an integer in a certain base.
Input starts with an integer T (≤ 50000), denoting the number of test cases.
Each case begins with two integers n (0 ≤ n ≤ 10^{6}) and base (2 ≤ base ≤ 1000). Both of these integers will be given in decimal.
For each case of input you have to print the case number and the digit(s) of factorial n in the given base.
Sample Input |
Output for Sample Input |
5 5 10 8 10 22 3 1000000 2 0 100 |
Case 1: 3 Case 2: 5 Case 3: 45 Case 4: 18488885 Case 5: 1 |
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