# Huge GCD

# Huge GCD

Gayasen has received a homework assignment to compute the greatest common divisor of the two positive integers `A`

and `B`

. Since the numbers are quite large, the professor provided him with `N`

smaller integers whose product is `A`

, and `M`

integers with product `B`

.
He would like to verify result, so he has asked you to write a program to solve his problem. But instead of printing complete answer you have to print answer modulo 10^{9}+7.

**Input**

First line of input contains the positive integer `N`

(1 <= N <= 1000).

Second line of input contains `N`

space-separated positive integers not greater than 10^{4}, whose product is the number `A`

.

Third line of input contains the positive integer `M`

(1 <= M <= 1000).

Fourth line of input contains `M`

space-separated positive integers not greater than 10^{4}, whose product is the number `B`

.

**OUTPUT**

Print the greatest common divisor of numbers `A`

and `B`

modulo `1000000007`

.

**Constraints**

1 <= N, M <= 1000

1 <= element of list <= 10000

**Sample Input #00**

```
5
2 2 3 3 25
4
8 1 6 170
```

**Sample Output #00**

```
60
```

**Sample Input #01**

```
13
1 2 4 8 32 64 128 256 512 1024 2048 4096 8192
9
1 3 9 27 81 243 729 2187 6561
```

**Sample Output #01**

```
1
```

**Sample Input #02**

```
3
2 3 5
2
4 5
```

**Sample Output #02**

```
10
```

**Explanation**

*Sample Case #00:* Here `A = 2×2×3×3×25 = 900`

, while `B = 8×1×6×170 = 8160`

. Greatest common divisor of `900`

and `8160`

is `60`

.

*Sample Case #01:* In first list all number are of form `2^a`

and in second they are of form `3^a`

. As these two list doesn't share any factor, their gcd is 1.

*Sample Case #02:* The greatest common divisor of numbers `A(=30)`

and `B(=20)`

equals `10`

.