Mancunian And Multiplicative Queries
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## Mathematics, Number theory, Sqrt-Decomposition

Problem
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Mancunian is in a hurry! He is late for his date with Nancy. So he has no time to deal with a long and complex problem statement.
You are given two arrays, A and $FUNC$. Each element of either array, $A_i$ or $FUNC_i$, is a positive integer not greater than C. Given Q queries, each of the form L R, the answer for each query is \begin{equation} \prod_{i=1}^{C} FUNC[cnt_i] \end{equation} where $cnt_i$ is the frequency of the integer i in the range L R.
The answer to the problem is the product of the answers of all the individual queries modulo $10^9+7$.

### Input format

The first line contains three integers N, C and Q denoting the size of the array, the range of allowed values for each array element and the number of queries respectively.
The second line contains N positive integers, denoting the elements of the array A. The $ith$ (1-indexed) of these represents $A_i$.
The third line contains $N+1$ positive integers, denoting the elements of the array $FUNC$. The $ith$ (0-indexed) of these represents $FUNC_i$.
The $ith$ of the next Q lines contains two integers, L and R for the $ith$ query.

### Output format

Print a single integer, which is the answer to the given problem.

### Constraints

• $1 \le N, Q \le 50,000$
• $1 \le C \le 1,000,000$
• $1 \le L \le R \le N$
SAMPLE INPUT
5 5 3
1 2 2 3 3
1 1 2 3 4 5
2 4
1 2
4 5
SAMPLE OUTPUT
4
Explanation

In the range specified by the first query, there are 0 occurrences of 1, 2 occurrences of 2, 1 occurrence of 3 and 0 occurrences of both 4 and 5. So the answer for the first query is $FUNC$ * $FUNC$ * $FUNC$ * $FUNC$ * $FUNC$ $=$ 2.

In the range specified by the second query, there is 1 occurrence of 1, 1 occurrence of 2, 0 occurrences of 3 and 0 occurrences of both 4 and 5. So the answer for the second query is $FUNC$ * $FUNC$ * $FUNC$ * $FUNC$ * $FUNC$ $=$ 1.

In the range specified by the third query, there are 0 occurrences of 1, 0 occurrences of 2, 2 occurrences of 3 and 0 occurrences of both 4 and 5. So the answer for the third query is $FUNC$ * $FUNC$ * $FUNC$ * $FUNC$ * $FUNC$ $=$ 2.

Hence the final answer is 2 * 1 * 2 $=$ 4.

Time Limit: 5.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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