In a football championship, N teams are competing against each other on the league stage. The current number of points of each team are X₁, X₂, X₃....X_N. M days of league stage are remaining and on each day K teams win and each of the winning team's points is incremented by 1. Top B teams will qualify for the playoffs in the championship. Officials of the tournament want to how many teams have a non-zero probability of making it to the playoffs.

Note: If points of certain teams are equal, any of the teams can qualify for playoffs and each team has equal probability.

Input format

The first line contains an integer T denoting the number of test cases. For each test case:
The first line contains four space-separated integers N, M, K, and B.
The second line contains N space-separated integers X₁, X₂, X₃...X_N.

Output format

Print T integers. For each test case:

Print the number of teams that have a non-zero probability of making it to the playoffs.

Constraints

\( 1\leq T \leq 20000\)
\(1 \leq N \leq 200000\)
\(1 \leq M \leq 10^9\)
\(1 \leq B,K < N\)
\( 1 \leq X_i \leq 10^9\)
Sum of N over all test cases will not exceed 200000.