You are given an array of (n) integers (a_1,a_2,\ldots,a_n). You are also given an array (p_1, p_2, \ldots, p_n). Let (S) denote the random multiset (i. e., it may contain equal elements) constructed as follows: Initially, (S) is empty. For each (i) from (1) to (n), insert (a_i) into (S) with probability (\frac{p_i}{10^4}). Note that each element is inserted independently. Denote (f(S)) as the bitwise XOR of all elements of (S). Please calculate the expected value of ((f(S))^2). Output the answer modulo (10^9 + 7). Formally, let (M = 10^9 + 7). It can be shown that the answer can be expressed as an irreducible fraction (\frac{p}{q}), where (p) and (q) are integers and (q \not \equiv 0 \pmod{M}). Output the integer equal to (p \cdot q^{-1} \bmod M). In other words, output such an integer (x) that (0 \le x < M) and (x \cdot q \equiv p \pmod{M}). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((1 \le n \le 2 \cdot 10^5)). The second line of each test case contains (n) integers (a_1,a_2,\ldots,a_n) ((1 \le a_i \le 1023)). The third line of each test case contains (n) integers (p_1,p_2,\ldots,p_n) ((1 \le p_i \le 10^4)). It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, output the expected value of ((f(S))^2), modulo (10^9 + 7). In the first test case, (a = 1, 2) and each element is inserted into (S) with probability (\frac{1}{2}), since (p_1 = p_2 = 5000) and (\frac{p_i}{10^4} = \frac{1}{2}). Thus, there are (4) outcomes for (S), each happening with the same probability of (\frac{1}{4}): (S = \varnothing). In this case, (f(S) = 0), $$$(f(S))