Problem Statement

There are $N$ colors $1,~2,~\cdots,~N$. There is also a bag that contains, for each $i$, $x_i$ balls painted in color $i$.

You take balls out of the bag one at a time until the bag is empty, and line them up in a row. Here, each ball is equally likely to be taken out.

Next, you split the row at every place where balls of different colors are adjacent. The number of contiguous subarrays obtained by this operation is called the discontinuity of the row.
Under the constraints of this problem, it can be proved that the expected value of the discontinuity of the resulting row is a rational number. Find this value $\mod (10^9+7)$.

• Definition of a rational number $\mod (10^9+7)$

Under the constraints of this problem, it can be shown that when the expected value to be found is expressed as an irreducible fraction $\frac{P}{Q}$ using coprime positive integers $P,~Q$, $Q$ is not divisible by $10^9+7$, and that an integer $R$ between $0$ and less than $10^9+7$ satisfying $P \equiv Q\times R \mod (10^9+7)$ is uniquely determined. Find this $R$.

Input

$N$
$x_1~\cdots~x_N$

All input values are integers and satisfy the following constraints.

• $1\leq N \leq 10^5$
• $1 \leq x_i$
• $\displaystyle \sum_{i=1}^N x_i \leq 10^{9}$

Output

Output the expected value of the discontinuity of the resulting row $\mod (10^9+7)$. Print a newline at the end.

Sample

2
2 1

333333338

1
100

1

4
1 1 1 1

4

10
3 1 4 1 5 9 2 6 5 3

384615422