You are given a base B and a number N. You have to find X such that Log_B(N) = X.

Input

The first line of input consists of the number of test cases T <= 100. The following T lines contain the two integers base B and number N. 0 <= B, N <= 10¹⁸.

Output

Print the test case number then X with 5 decimal places (see the example for the exact format). If X doesn't exist, print "Math Error!". Print a new line for each test case.

Example

Input:
3
2 8
4 16
9 27

Output:
Case 1: 3.00000
Case 2: 2.00000
Case 3: 1.50000