Bob has an array \(A\) of size \(N\), and he is very fond of two integers \(X\) and \(Y\). Find the length of the longest subarray, such that it contains exactly \(X\) distinct integers and \(Y\) exist at least once in the subarray.

Input format

The first line contains an integer \(T\), which denotes the number of test cases.
The first line of each test case contains three space separated integers \(N\), \(X\), \(Y\) denoting the size of array \(A\), the value of \(X\) and \(Y\), respectively.
The second line of each test case contains \(N\) space-separated integers, denoting the elements of array \(A\).

Output format

For each test case, print the length of the largest subarray, such that it contains exactly \(X\) distinct integers and \(Y\) exist at least once in the subarray in a new line.

Constraints

\(1 \leq T \leq 10 \\ 1 \leq N \leq 10^5 \\ 0 \leq A[i] \leq 10^5 \\ 1 \leq X, Y \leq 10^5\)