201220: [AtCoder]ARC122 A - Many Formulae

Memory Limit:1024 MB Time Limit:2 S
Judge Style:Text Compare Creator:
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Description

Score : $400$ points

Problem Statement

You are given a sequence of $N$ non-negative integers: $A_1,A_2,\cdots,A_N$.

Consider inserting a + or - between each pair of adjacent terms to make one formula.

There are $2^{N-1}$ such ways to make a formula. Such a formula is called good when the following condition is satisfied:

  • - does not occur twice or more in a row.

Find the sum of the evaluations of all good formulae. We can prove that this sum is always a non-negative integer, so print it modulo $(10^9+7)$.

Constraints

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

Input

Input is given from Standard Input in the following format:

$N$
$A_1$ $A_2$ $\cdots$ $A_N$

Output

Print the sum modulo $(10^9+7)$.


Sample Input 1

3
3 1 5

Sample Output 1

15

We have the following three good formulae:

  • $3+1+5=9$

  • $3+1-5=-1$

  • $3-1+5=7$

Note that $3-1-5$ is not good since- occurs twice in a row in it. Thus, the answer is $9+(-1)+7=15$.


Sample Input 2

4
1 1 1 1

Sample Output 2

10

We have the following five good formulae:

  • $1+1+1+1=4$

  • $1+1+1-1=2$

  • $1+1-1+1=2$

  • $1-1+1+1=2$

  • $1-1+1-1=0$

Thus, the answer is $4+2+2+2+0=10$.


Sample Input 3

10
866111664 178537096 844917655 218662351 383133839 231371336 353498483 865935868 472381277 579910117

Sample Output 3

279919144

Print the sum modulo $(10^9+7)$.

Input

题意翻译

### 题目描述 给出长度为 $ N $ 的非负整数序列 $ A_1,A_2,\cdots,A_N$。 考虑在此序列的相邻 $ 2 $ 项之间放置 `+` 或 `-` 以创建一个表达式。 有 $ 2^{N-1}$ 创建表达式的方法,但我们会将满足以下条件的表达式称为**好表达式**。 - `-` 连续出现不超过 $ 2 $ 次。 求所有良好表达式值的总和。 可以证明,这个值始终是一个非负整数。因此,输出此值对 $ 10^9+7 $ 取模的结果。 ### 输入格式 输入由以下格式给出: > $ N\ A_1\ A_2\ \cdots\ A_N$

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