Problem Statement

Charo, Senpai.
I finally bought the latest VR game, "Ambition of the yukicoder Kingdom"!
For summer vacation, I, Meguru, am planning to travel around the yukicoder Kingdom several times, so I intend to hole up in a dungeon for now and earn my travel money.
Senpai, please calculate how much I need to earn!

The yukicoder Kingdom has $N$ towns and $N-1$ roads, you see.
The $k$-th road connects town $A_k$ and town $B_k$, and every town can be reached from every other town by passing through some roads.
Each of my trips goes from some town $X$ to some town $Y$ by road, and I plan to stay one night and go sightseeing in every town I visit, including towns $X,Y$.
Right now, staying in town $k$ costs $S_k$, but King yuki has parades scheduled this summer vacation, so the lodging costs are going to change...

Each town $k$ has a value called the inflation coefficient, $C_k$.
When the king holds a parade of scale $Z$ from town $X$ to town $Y$, the lodging costs of the towns the parade passed through, including towns $X,Y$, go up and stay that way from then on.
What's more, each one goes up by that town's inflation coefficient multiplied by $Z$, which is really harsh...

Between now and the end of summer vacation, there are $Q$ scheduled events in total, counting my trips and the parades.
I've labeled them in chronological order as event $1$, event $2$, $\ldots$, event $Q$, and each one is written in my notes in one of the following formats!

• $0\ X\ Y\ Z$: The king's parade of scale $Z$ is held from town $X$ to town $Y$.
• $1\ X\ Y$: Meguru plans to travel from town $X$ to town $Y$!

By the way, King yuki's parades are really gorgeous and fun, you know.
Would you like to go see one with me sometime?
Uh..., right, I guess not...

Input

$N$
$S_1$ $S_2$ $\cdots$ $S_N$
$C_1$ $C_2$ $\cdots$ $C_N$
$A_1$ $B_1$
$A_2$ $B_2$
$\quad \vdots$
$A_{N-1}$ $B_{N-1}$
$Q$
予定 $1$
予定 $2$
$\quad \vdots$
予定 $Q$

Here, event $k$ is in one of the following formats:

$0$ $X_k$ $Y_k$ $Z_k$

or

$1$ $X_k$ $Y_k$

That's all!

$2 \leq N \leq 200000 = 2 \times 10^5$
$0 \leq S_k, C_k \leq 1000000006 = 10^9+6$
$1 \leq A_k, B_k \leq N, \;\; A_k \neq B_k$
$1 \leq Q \leq 200000 = 2 \times 10^5$
$1 \leq X_k, Y_k \leq N, \;\; X_k \neq Y_k$
$0 \leq Z_k \leq 1000000006 = 10^9+6$

Output

For each trip event, please output the lodging cost needed for that trip, assuming everything goes as scheduled, modulo ${\rm mod}\ 1000000007$!

Sample

8
1 2 3 4 5 6 7 8
8 7 6 5 4 3 2 1
6 1
1 5
1 3
2 7
2 1
2 4
8 4
6
1 1 7
1 8 5
0 6 3 100
1 5 3
0 7 5 10000
1 6 8

10
20
1409
151121