Description

A number is perfect if and only if it is equal to the sum of all its divisors that are smaller than it.

For example, $28 = 1 + 2 + 4 + 7 + 14$, so $28$ is perfect.

Based on this, we define the imperfection value $F(N)$ of a number, which is the absolute value of the difference between $N$ and the sum of all divisors of $N$ that are smaller than $N$.

For example, $F(6)=|6-1-2-3|=0$.

$F(11)=|11-1|=10$.

$F(24)=|24-1-2-3-4-6-8-12|=|-12|=12$.

Now you are given two positive integers $A$ and $B$. Please compute $F(A)+F(A+1)+...+F(B)$.

Input Format

One line with two integers $A$ and $B$, as described above.

Output Format

One line with one integer, representing $F(A)+F(A+1)+...+F(B)$.

1 9

21

24 24

12

Hint

Sample Explanation #1

$F(1)+...+F(9)=1+1+2+1+4+0+6+1+5=21$.

Constraints

For $100\%$ of the testdata, $1 \le A,B \le 10^7$.

Notes

The score of this problem follows the original COCI settings, with a full score of $120$.

Translated from COCI2016_2017 CONTEST #6 T4 SAVRSEN.

Translated by ChatGPT 5