Stairs and Lines
题意翻译
给定一个最多有 $7$ 阶的阶梯，高度为 $i$ 的阶梯宽度为 $w_i$ ，现在你需要给阶梯上网格的边缘上色，要求最外层的边缘必须上色，且不能使任意一个 $1 \times 1$ 的小正方形四个边都被上色。求方案数对 $10^9+7$ 取模。
题目描述
You are given a figure on a grid representing stairs consisting of 7 steps. The width of the stair on height $ i $ is $ w_{i} $ squares. Formally, the figure is created by consecutively joining rectangles of size $ w_{i}×i $ so that the $ w_{i} $ sides lie on one straight line. Thus, for example, if all $ w_{i}=1 $ , the figure will look like that (different colors represent different rectangles):
And if $ w={5,1,0,3,0,0,1} $ , then it looks like that:
Find the number of ways to color some borders of the figure's inner squares so that no square had all four borders colored. The borders of the squares lying on the border of the figure should be considered painted. The ways that differ with the figure's rotation should be considered distinct.
输入输出格式
输入格式
The single line of the input contains 7 numbers $ w_{1},w_{2},...,w_{7} $ ( $ 0<=w_{i}<=10^{5} $ ). It is guaranteed that at least one of the $ w_{i} $ 's isn't equal to zero.
输出格式
In the single line of the output display a single number — the answer to the problem modulo $ 10^{9}+7 $ .
输入输出样例
输入样例 #1
0 1 0 0 0 0 0
输出样例 #1
1
输入样例 #2
0 2 0 0 0 0 0
输出样例 #2
7
输入样例 #3
1 1 1 0 0 0 0
输出样例 #3
9
输入样例 #4
5 1 0 3 0 0 1
输出样例 #4
411199181
说明
All the possible ways of painting the third sample are given below:
