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

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