U-turn bits

Let n = 2^s, where s \geq 0 is an integer. For each integer $i$ from $0$ to n-1, define the value a_i as follows. Let b_{s-1}\ldots b_1b_0 be the binary representation of $i$ (padded on the left with zeros if necessary to reach length $s$). Reverse these bits to obtain b_0b_1\ldots b_{s-1}. Then a_i is the integer whose binary representation is b_0b_1\ldots b_{s-1}.

For example, if s = 3, i = 3, then the binary representation is 011_2, and the reversed is 110_2. Therefore, if s = 3, a_3 = 6.

For a given $s$, you are required to efficiently answer queries to compute the sum a_l + a_{l+1} + \ldots + a_r modulo $1000000007$.