Različitost

Two infinite periodic sequences of integers, $a_i$ and $b_i$, are given, defined by their periods of lengths $n$ and $m$, respectively. This means that the natural numbers $n$ and $m$ are given, as well as the numbers $a_1, a_2, \dots , a_n$ and $b_1, b_2, \dots , b_m$, for which $a_i = a_{i+n}$ and $b_i = b_{i+m}$ hold for every natural number $i$.

Additionally, given a natural number $k$, we define the "diversity" of these two sequences as the sum $a_i \oplus b_i$ for each $i = 1, 2, \dots , k$. (Here, $\oplus$ denotes the bitwise exclusive OR operation, which produces ones in the positions where the binary digits of the two numbers differ. For example, $5 \oplus 3 = (101)_2 \oplus (011)_2 = (110)_2 = 6$.)

Your task is to calculate the diversity of the given sequences.

In the first line, there are $n$, $m$, and $k$ ($1 ≤ n, m ≤ 2 \cdot 10^5$, $1 ≤ k ≤ 10^{18}$), which are the numbers from the task description.

In the second line, there are $n$ integers $a_1, \dots , a_n$ ($0 ≤ a_i ≤ 10^{18}$, $i = 1, 2, \dots , n$).

In the third line, there are $m$ integers $b_1, \dots , b_m$ ($0 ≤ b_i ≤ 10^{18}$, $i = 1, 2, \dots , m$).

Because the answer can be very large, output the remainder of the answer when divided by $10^9 + 7$ in a single line.