Hints: Divisibility by 2^n

Hint 1 ↕

Any number can be written as

num = 2^x * remain

What happens to the product? What is the criteria for divisibility by 2^n?

Hint 2 ↕

Suppose the exponent of 2 in the resulting product is x. Then, you need

want = max(0, n - x)

Which index gives you the maximum benefit?

Hint 3 ↕

Compute the exponent of 2 for each index, sort them in descending order and greedily keep taking the largest exponent till you reach your goal.