powers.i from 0 to 30, check if the ith bit of n is set. If it is, append 2^i to powers.powers modulo 10^9 + 7 and store them in a list prefix_products.answers to store the results of the queries.[left, right] in queries, calculate the product for the range:
left is 0, append prefix_products[right] to answers.prefix_products[left - 1] and multiply it with prefix_products[right], then append the result modulo 10^9 + 7 to answers.answers.