On the occasion of your birthday, your friends have organized a surprise birthday party for you. In that party, there is a game planned by them. Rules of the game are as follows:-

1. There is a cake, in the shape of a rectangle, of length $m$ and width $n$.
2. Each cut on this cake has a given cost, $cost\_x[i]$ and $cost\_y[i]$ for each cut along a row and a column respectively. This means that the cost of a cut must be multiplied by the number of segments it crosses.
3. You have to cut the cake into $1 \times 1$ slices such that the cost of cutting is minimum.
4. The cost of cutting the whole cake down into $1 \times 1$ slices is the sum of the costs of each successive cut.

Can you find this minimum cost? The number may be large, so print the value $modulo \ 10^9 + 7$.

Input Format:

The first line contains an integer q, the number of input queries.

The following q  sets of lines are as follows:

• The first line has two positive space-separated integers $m$ and $n$, the number of rows and columns on the cake.

• The second line contains  $m-1$  space-separated integers $cost\_y[i]$, the cost of a horizontal cut between rows $i$, and $i+1$  of the cake.

• The third line contains $n-1$ space-separated integers $cost\_x[j]$, the cost of a vertical cut between columns  $j$and $j+1$  of the cake.

Output Format:

For each of the q queries, find the minimum cost of cutting the cake into $1\times1$ squares and print the value of this cost module $10^9 + 7$

Constraints:

$1 \leq q \leq 200$

$2 \leq m,n \leq 100000$

$0 \leq cost\_x[j], cost\_y[i]\leq10^9$