Swallowed Diagonals in N-Dimensional Space

Given an $n$-dimensional space, where the size of the $i$\text{-th} dimension is $m_i$. Each position is represented by coordinates $$(x_1, x_2, \dots, x_n)$$ with $x_i\in[1,m_i]$. There is a black hole at position $$(a_1,a_2,\dots,a_n)$$. A position $$(b_1,b_2,\dots,b_n)$$ is on the same diagonal as the black hole if and only if there exists an integer $k\ge0$ such that for every $1\le i\le n$,

All positions on the same diagonal (including the black hole itself) will be swallowed. Compute the number of positions swallowed modulo $10^9+7$.

inputFormat

The input consists of three lines:

1. The first line contains an integer $n$, the number of dimensions.
2. The second line contains $n$ integers $m_1, m_2, \dots, m_n$, representing the size of each dimension.
3. The third line contains $n$ integers $a_1, a_2, \dots, a_n$, representing the coordinates of the black hole.

outputFormat

Output a single integer, the number of positions swallowed by the black hole modulo $10^9+7$.

sample

1
5
3

5