You are given an array A containing N integers. Find if it is possible to choose exactly M elements from the array such that the MEX of the chosen elements is exactly K.

Recall that the MEX of an array is the smallest non-negative integer that does not belong to the array. For example, the MEX of [2, 2, 1] is 0 because 0 does not belong to the array, the MEX of [3, 1, 0, 1] is 2 because 0 and 1 belong to the array, but 2 does not.

------ Input Format ------

• The first line contains an integer T, denoting the number of test cases. The T test cases then follow:
• The first line of each test case contains an integer N, M, K, denoting the length of the array, the number of elements to be chosen, and the required MEX respectively.
• The second line of each test case contains $N space-separated integers A_{1},A_{2},\ldots,A_{N},$ denoting the elements of the array.

------ Output Format ------

For each test case, print YES if it is possible to choose M elements from the array A so that the MEX of the chosen elements is exactly K and NO otherwise.

You may print each character of the string in uppercase or lowercase (for example, the strings yEs, yes, Yes and YES will all be treated as identical).

------ Constraints ------

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 100$
$1 ≤ M ≤ N$
$0 ≤ A_{i}, K ≤ N$

----- Sample Input 1 ------
6
5 4 2
0 1 3 0 3
2 1 2
0 1
3 3 3
0 1 2
4 3 3
2 0 4 3
5 4 2
0 2 1 2 5
6 5 2
0 1 0 2 0 3

----- Sample Output 1 ------
YES
NO
YES
NO
NO
YES

----- explanation 1 ------
Test case $1$: The chosen elements are $0, 1, 3, 0$ and $MEX([0, 1, 3, 0]) = 2$.

Test case $3$: The chosen elements are $0, 1, 2$ and $MEX([0, 1, 2]) = 3$.

Test case $6$: The chosen elements are $0, 1, 0, 0, 3$ and $MEX([0, 1, 0, 0, 3]) = 2$.

Test case $2, 4, 5$: There is no way to choose elements to obtain the required MEX.

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