Many Formulae

AtCoder

IDarc122_a

Time2000ms

Memory256MB

Difficulty—

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: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

3
3 1 5

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 $9+(-1)+7=15$.

Input #2

4
1 1 1 1

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 $4+2+2+2+0=10$.

Input #3

10
866111664 178537096 844917655 218662351 383133839 231371336 353498483 865935868 472381277 579910117

Output #3

279919144

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

API Response (JSON)

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