Given an array A of N elements. You can apply the given operations on array A.

• Type 1: Choose an index i (1 ≤ i ≤ N) and set A[i] = A[i] - 1.
• Type 2: Choose an index i (1 ≤ i ≤ N) and set A[i] = 0.

Find the maximum length subarray in array ​A​​​​​​ where all the elements in the subarray is 0 by using at most X operations of Type 1 and Y operations of Type 2.

Note

• Assume 1-based indexing.

Input

• The first line contains an integer T denoting the number of test cases.
• For each test case:
  • The first line contains 3 space-separated integers N, X, Y.
  • Next line contains N space-separated integers denoting the elements of array A.

Output

For each test case in a new line, print the maximum length subarray in A where all the elements in the subarray is 0. 

Constraints

\(1 ≤ T ≤ 5\\ 1 ≤ N ≤ 10^5\\ 0 ≤ X ≤ 10^{14}\\ 0 ≤ Y ≤ 10^9\\ 0 ≤ A[i] ≤ 10^9\)