A Bit Fun

Time Limit: 2 s Memory Limit: 256 MB

Submission：44 AC：8 Score：99.62

Description

There are n numbers in a array, as a₀, a₁ ... , a_n-1, and another number m. We define a function f(i, j) = a_i|a_i+1|a_i+2| ... | a_j . Where "|" is the bit-OR operation. (i <= j)
The problem is really simple: please count the number of different pairs of (i, j) where f(i, j) < m.

Input

The first line has a number T (T <= 50), indicating the number of test cases.

For each test case, first line contains two numbers n and m.(1 <= n <= 1e5, 1 <= m <= 2³⁰) Then n numbers come in the second line which is the array a, where 1 <= a_i <= 2³⁰.

Output

For every case, you should output "Case #t: " at first, without quotes. The t is the case number starting from 1.
Then follows the answer.

Samples

input

2 3 6 1 3 5 2 4 5 4

output

Case #1: 4 Case #2: 0

Hint

HDU-4737 加强了数据

Author

PAN, Lyuzhi