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

\(1 \le N, Q \le 50,000\)
\(1 \le C \le 1,000,000\)
\(1 \le L \le R \le N\)