東京海上日動 プログラミングコンテスト2021 (AtCoder Regular Contest 122)
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Problem Statement
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You are given a sequence of $N$ non-negative integers: $A_1,A_2,\cdots,A_N$.
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Consider inserting a + or - between each pair of adjacent terms to make one formula.
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There are $2^{N-1}$ such ways to make a formula. Such a formula is called good when the following condition is satisfied:
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-does not occur twice or more in a row.
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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 $(10^9+7)$.
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Constraints
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$1 \leq N \leq 10^5$$1 \leq A_i \leq 10^9$- All values in input are integers.
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Input
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Input is given from Standard Input in the following format:
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N
A_1 A_2 \cdots A_N翻译中…
Output
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Print the sum modulo $(10^9+7)$.
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样例
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 $(10^9+7)$.
题目信息
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