E. Fill the Matrixtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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?InputThe 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.OutputFor 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.ExampleInput
630 0 0942 0 3 1542 0 3 1642 0 3 110100 2 2 1 5 10 3 4 1 120110Output
6
3
4
4
16
0

630 0 0942 0 3 1542 0 3 1642 0 3 110100 2 2 1 5 10 3 4 1 120110
6 3 4 4 16 0 
['data structures', 'greedy', 'math', '*2200']