You have pills of characteristic values .
On each day you can take the th pill and increase your health by points or Do nothing and take 1 point of damage , where is a value deenoting your health. You die if your health becomes zero. Initially (where is a value given in the input).
What is the minimum number of pills you should take to survive for days.
Input
Each test consists of multiple test cases. The first line contains a single integer ( ) — the number of test cases. Description of the test cases follows.
The first line of each test case contains two integers and where
The second line of each test case contains space seperated integers ( )
The sum of over all test cases does not exceed .
Output
For each test case print the minimum number of pills you should take to survive for days.
In the first test case, you must take , and pills to survive.