Score : $300$ points

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.

3
3 5 2
26

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 $8$.

4
12 34 56 78
1000

23