Problem Statement

We have a sequence of $N$ positive integers: $A=(A_1,\\dots,A_N)$.
Let $B$ be the concatenation of $10^{100}$ copies of $A$.

Consider summing up the terms of $B$ from left to right. When does the sum exceed $X$ for the first time?
In other words, find the minimum integer $k$ such that:

$\\displaystyle{\\sum_{i=1}^{k} B_i \\gt X}$.

Constraints

• $1 \\leq N \\leq 10^5$
• $1 \\leq A_i \\leq 10^9$
• $1 \\leq X \\leq 10^{18}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $A_1$ $\\ldots$ $A_N$ $X$

Output

Print the answer.

Sample Input 1

3
3 5 2
26

Sample Output 1

8

We have $B=(3,5,2,3,5,2,3,5,2,\\dots)$.
$\\displaystyle{\\sum_{i=1}^{8} B_i = 28 \\gt 26}$ holds, but the condition is not satisfied when $k$ is $7$ or less, so the answer is $8$.

Sample Input 2

4
12 34 56 78
1000

Sample Output 2

23