Sanghyeon's Math Study Plan

A teacher at KSA likes students who study math hard, so the teacher has decided to make students study a lot of math over the next $N$ days. The teacher wants a student to solve $A_i$ math problems on day $i$. The teacher's favorability toward a student depends on how many problems the student solved that day. If a student solved $x$ problems on day $i$, the favorability increases by the following amount.

$f_i(x) = \begin{cases} x & \text{if } x \ge A_i, \\ 2(x - A_i) & \text{if } x < A_i \end{cases}$

Sanghyeon wants a regular routine, so he decides to solve the same number of math problems every day for $N$ days. At first, the teacher's favorability toward Sanghyeon is $0$. Sanghyeon wants a favorability of at least $L$ after $N$ days. Find the minimum number of problems he must solve per day.

The first line contains an integer $N$ ($1 \le N \le 10^5$). The second line contains $N$ integers $A_1, A_2, \cdots, A_N$ separated by spaces ($1 \le A_i \le 10^4$). The third line contains an integer $L$ ($1 \le L \le 10^9$).

Print the minimum number of math problems Sanghyeon must solve per day.