Mod Mod Mod
题意翻译
$$f(x,n) = x \mod a_n$$
$$f(x,i) = ( x \mod a_i ) + f(x \mod a_i,i+1)$$
给出a序列,当x取遍所有非负整数时$f(x,1)$的最大值。
题目描述
You are given a sequence of integers $ a_{1},a_{2},...,a_{n} $ . Let ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF889E/babd3332060a4ee6973a9fa3f688c744930d9a0a.png), and ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF889E/3a61ca4726dc1db34df92b20859e100704661de5.png) for $ 1<=i<n $ . Here, ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF889E/609a42354b344d4b30f3720c48d42a71dbe37fb8.png) denotes the modulus operation. Find the maximum value of $ f(x,1) $ over all nonnegative integers $ x $ .
输入输出格式
输入格式
The first line contains a single integer $ n $ ( $ 1<=n<=200000 $ ) — the length of the sequence.
The second lines contains $ n $ integers $ a_{1},a_{2},...,a_{n} $ ( $ 1<=a_{i}<=10^{13} $ ) — the elements of the sequence.
输出格式
Output a single integer — the maximum value of $ f(x,1) $ over all nonnegative integers $ x $ .
输入输出样例
输入样例 #1
2
10 5
输出样例 #1
13
输入样例 #2
5
5 4 3 2 1
输出样例 #2
6
输入样例 #3
4
5 10 5 10
输出样例 #3
16
说明
In the first example you can choose, for example, $ x=19 $ .
In the second example you can choose, for example, $ x=3 $ or $ x=2 $ .