Range Product Queries of Powers

To solve this problem, we need to first generate the powers array for the given integer n. We can do this by taking the binary representation of n, which will contain a series of 0s and 1s. We can add (2^i) to the powers array for each bit in position i that is set to 1.

Once we have the powers array, we can calculate the result for each query by multiplying the values from the left to the right indices given in the query.

Here’s the Python code:

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class Solution:
    def productQueries(self, n: int, queries: List[List[int]]) -> List[int]:
        MOD = 10**9 + 7

        # Generate the powers array from the binary representation of n
        powers = []
        i = 0
        while n > 0:
            if n % 2 == 1:
                powers.append(2**i)
            n = n // 2
            i += 1

        # Calculate the result for each query
        results = []
        for query in queries:
            left, right = query
            product = 1
            for j in range(left, right + 1):
                product *= powers[j]
                product %= MOD
            results.append(product)

        return results

The code first constructs the powers array by examining the binary representation of n. Then, it iterates through the queries, multiplying the values from the left to the right index for each query, and adding the result to the results array.

This solution takes into account the constraints and returns the answer modulo (10^9 + 7) as required.