Problem Statement

$N$ people played rock-paper-scissors using the hands Rock, Scissors, and Paper. For each of the $N$ participants, the probabilities of playing Rock, Scissors, and Paper are $\dfrac{A_G}{B_G},\dfrac{A_C}{B_C},\dfrac{A_P}{B_P}$, respectively. Also, the hands played by the $N$ people are independent. Let $R$ be the probability that the game ends in a draw. It can be shown that $R$ is a rational number; print this $R$ ${\rm mod} (10^9+7)$ in the way described in the notes below.

Solve $T$ test cases.

Notes

Printing the probability $R$ ${\rm mod} (10^9+7)$ means the following: when $R=\dfrac{P}{Q}$ ($P,Q$: integers, $Q$ is not a multiple of $10^9+7$ ), print the integer that is at least $0$ and less than $10^9+7$, $S$, satisfying $SQ \equiv P \pmod{10^9+7}$. Under the constraints of this problem, there exists at least 1 pair of integers $P,Q$ satisfying $R=\dfrac{P}{Q}$ ($P,Q$: integers, $Q$ is not a multiple of $10^9+7$ ).

Constraints

• $1 \leq T \leq 10^4$
• $2 \leq N \leq 10^{18}$
• $0 \leq A_G \leq B_G \leq 10^9$
• $0 \leq A_C \leq B_C \leq 10^9$
• $0 \leq A_P \leq B_P \leq 10^9$
• $B_G,B_C,B_P \neq 0$
• $\dfrac{A_G}{B_G}+\dfrac{A_C}{B_C}+\dfrac{A_P}{B_P}=1$
• All input values are integers.

Input

$T$

$N~A_G~B_G~A_C~B_C~A_P~B_P$

Sample

5
2 1 3 1 3 1 3
2 1 2 1 3 1 6
3 1 3 1 3 1 3
4 1 5 2 5 4 10
5 1 1 0 1 0 1

333333336
388888892
333333336
937600007
1