Background

Smart has recently become obsessed with the study of divisors.

Problem Description

For a number $X$, the function $f(X)$ denotes the sum of all divisors of $X$. For example, $f(6)=1+2+3+6=12$. For a given $X$, Smart can quickly compute $f(X)$. Now, given two positive integers $X$ and $Y$ ($X<Y$), Smart wants to quickly compute the value of $f(X)+f(X+1)+\dots+f(Y)$. Can you help Smart compute this value?

Input Format

The input contains only one line with two positive integers $X$ and $Y$ ($X<Y$), indicating that you need to compute $f(X)+f(X+1)+\dots+f(Y)$.

Output Format

Output a single line containing the value of $f(X)+f(X+1)+\dots+f(Y)$.

2 4

14

123 321

72543

Hint

For $20\%$ of the testdata, $1 \leq X < Y \leq 10^5$. For $60\%$ of the testdata, $1 \leq X < Y \leq 1\times 10^7$. For $100\%$ of the testdata, $1 \leq X < Y \leq 2\times 10^9$.

Translated by ChatGPT 5