A curd manufacturing factory owns curd producing machines of different qualities. A curd producer of quality q produces 1 unit of curd in q units of time.

For example, a curd producer of quality 5 produces 1 unit of curd at time 5, 1 unit of curd at time 10 and so on.

Given the qualities of all the machines, find the minimum time required to produce T units of curd.

Input

The first line consists of an integer t, the number of test cases. For each testcase, the first line consists of 2 integers n and T, the number of machines and the target amount of curd. The next n lines consists of integers representing the qualities of the producer machines.

Output

For each test case, find the minimum time required to produce the target amount of curd.

Input Constraints:

1 <= t <= 10^2

1 <= n <= 10^4

1 <= T <= 10^9

1 <= quality of each machine <= 10^9

Note: Note that a quality 5 producer has produced only 1 curd at time 9 and not 1.8.

Sample

Input:
3
2 3
5
10
3 1000000
1
2
3
1 1000000000
1000000000
Output:
10
545455
1000000000000000000