You are given an array A that consists of N positive integers. A subset of the array A is good when the sum of the elements of the subset is K or greater.
An element of the array is unnecessary if for any good subset of the array containing i element, the set that can be obtained by eliminating i from the subset is also good.
Find the number of the unnecessary elements present in array A.
Input format
- The first line contains an integer T denoting the number of test cases.
- The first line of each test case contains two space-separated integers N and K.
- The second line of each test case contains N space-separated integers denoting array A.
Output format
For each test case, print the total number of unneccessary elements present in the array in a new line.
Constraints
1≤T≤101≤N≤50001≤K≤50001≤Ai≤5000
For the first testcase, there are two good sets: {2,3} and {1,2,3}.
Element 1 is only contained in {1,2,3}, and this set without element 1, {2,3}, is also good. Thus, element 1 is unnecessary.
For element 2, a good set {2,3} without element 2, {3}, is not good. Thus, element 2 is NOT unnecessary.
Neither is element 3 for a similar reason, hence the answer is 1.
For the second testcase, there is no good set. Therefore, all the elements are unnecessary.
