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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 $28$ is perfect because $28 = 1 + 2 + 4 + 7 + 14$.
Motivated by this definition, we introduce the metric of imperfection of number $N$, denoted with $f(N)$, as the absolute difference between $N$ and the sum of its divisors less than $N$. It follows that perfect numbers’ imperfection score is $0$, and the rest of natural numbers have a higher imperfection score. For example:
Write a programme that, for positive integers $A$ and $B$, calculates the sum of imperfections of all numbers between $A$ and $B$: $f(A) + f(A + 1) + \ldots + f(B)$.
The first line of input contains the positive integers $A$ and $B$ ($1 \le A \le B \le 10^7$).
The first and only line of output must contain the required sum.
Clarification of the first test case: $1 + 1 + 2 + 1 + 4 + 0 + 6 + 1 + 5$.