Numbers with Strength

One of the events at Quark'23 is a programming competition that challenges participants to solve a problem involving an array of numbers and their "strength". The strength of a number is defined as the maximum integer $x$ such that $2^x$ divides that number leaving no remainder. For example, the strength of 12 is 2 because it can be divided by 2 twice to get 3. The participants are given a total