There is a square matrix, consisting of $$$n$$$ rows and $$$n$$$ columns of cells, both numbered from $$$1$$$ to $$$n$$$. The cells are colored white or black. Cells from $$$1$$$ to $$$a_i$$$ are black, and cells from $$$a_i+1$$$ to $$$n$$$ are white, in the $$$i$$$-th column.

You want to place $$$m$$$ integers in the matrix, from $$$1$$$ to $$$m$$$. There are two rules:

each cell should contain at most one integer;
black cells should not contain integers.

The beauty of the matrix is the number of such $$$j$$$ that $$$j+1$$$ is written in the same row, in the next column as $$$j$$$ (in the neighbouring cell to the right).

What's the maximum possible beauty of the matrix?

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of testcases.

The first line of each testcase contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the size of the matrix.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le n$$$) — the number of black cells in each column.

The third line contains a single integer $$$m$$$ ($$$0 \le m \le \sum \limits_{i=1}^n n - a_i$$$) — the number of integers you have to write in the matrix. Note that this number might not fit into a 32-bit integer data type.

The sum of $$$n$$$ over all testcases doesn't exceed $$$2 \cdot 10^5$$$.

Output

For each testcase, print a single integer — the maximum beauty of the matrix after you write all $$$m$$$ integers in it. Note that there are no more integers than the white cells, so the answer always exists.

Fill the Matrix

Examples