Score : $300$ points

问题描述

我们有一个包含 $N$ 个正整数的序列：$A=(A_1,\dots,A_N)$。

令 $B$ 为 $A$ 的重复串联，重复次数为 $10^{100}$ 次。

从左至右计算序列 $B$ 中各项之和。何时和首次超过 $X$？

换句话说，找到满足以下条件的最小整数 $k$：

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

以上为通义千问 qwen-max 翻译，仅供参考。

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

update @ 2024/3/10 09:43:13