You are given an array of integer. You have to find the sum of all possible subsequences sum of the array. For example: The given array of length n = 3 is {1, 2, 3}. All the subsequences of this array with the corresponding array summations are:

The answer is 24.

Input

The first line of input will contain the test case T (1 <= T <= 10). There will be two lines for each test case. First line will contain the value of n (1 <= n <= 1000) and the next line will contain the array elements space-separated integers. Each integer will be between 1 and 1000000000.

Output

For each case of input, output the answer of the problem in the format "Case X: Y" where X denotes the number of the test case and Y denotes the answer. Answer could be very large so output the answer modulo 100000007.

Example

Input:
2
3
1 2 3
3
4 1 2

Output:
Case 1: 24
Case 2: 28