第五回日本最強プログラマー学生選手権-予選-（AtCoder Regular Contest 180）
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Problem Statement
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You are given an integer sequence $A=(A_1,A_2,\cdots,A_N)$ of length $N$.
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You will perform the following operation exactly once:
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- Choose a non-empty subsequence of
$A$(not necessarily contiguous) and replace it with its cumulative sums. More precisely, first choose a sequence of indices$(i_1,i_2,\cdots,i_k)$such that$1 \leq i_1 < i_2 < \cdots < i_k \leq N$. The length of the sequence$k$($1 \leq k \leq N$) can be chosen freely. Then, for each$j$($1 \leq j \leq k$), replace the value of$A_{i_j}$with$\sum_{1 \leq x \leq j} A_{i_x}$. This replacement is done simultaneously for all chosen indices.
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Find, modulo $10^9+7$, the number of possible sequences $A$ after the operation.
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Constraints
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$1 \leq N \leq 100$$-10 \leq A_i \leq 10$- All input values are integers.
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Input
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The 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 answer.
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样例
Input #1
3
1 1 2
Output #1
4
The possible sequences $A$ after the operation are as follows:
- $A=(1,1,2)$: This can be achieved with $k=1$ and $(i_1)=(1)$.
- $A=(1,2,2)$: This can be achieved with $k=2$ and $(i_1,i_2)=(1,2)$.
- $A=(1,1,3)$: This can be achieved with $k=2$ and $(i_1,i_2)=(1,3)$.
- $A=(1,2,4)$: This can be achieved with $k=3$ and $(i_1,i_2,i_3)=(1,2,3)$.
Input #2
4
1 -1 1 -1
Output #2
8
Input #3
5
0 0 0 0 0
Output #3
1
Input #4
40
2 -2 1 3 -3 -1 -2 -3 0 -1 -2 0 -3 0 0 2 0 -1 2 -2 -2 -1 3 -2 -2 -2 2 3 2 -3 0 -2 2 1 3 0 -1 0 -2 -3
Output #4
420429545
题目信息
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（CI 管线），如有出入请以原文为准。