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A number is perfect if it is equal to the sum of its divisors, the ones that are smaller than it. For example, number is perfect because .
Motivated by this definition, we introduce the metric of imperfection of number , denoted with , as the absolute difference between and the sum of its divisors less than . It follows that perfect numbers’ imperfection score is , and the rest of natural numbers have a higher imperfection score. For example:
Write a programme that, for positive integers and , calculates the sum of imperfections of all numbers between and : .
The first line of input contains the positive integers and ().
The first and only line of output must contain the required sum.
Clarification of the first test case: .