Problem Background

Smart has recently become obsessed with the study of divisors.

Problem Description

For a number \( X \), the function \( f(X) \) represents the sum of all divisors of \( X \). For example: \( f(6) = 1 + 2 + 3 + 6 = 12 \). Given a number \( X \), Smart can quickly calculate \( f(X) \). The problem now is, given two positive integers \( X \) and \( Y \) where \( X < Y \), Smart wants to quickly calculate the value of \( f(X) + f(X+1) + \ldots + f(Y) \). Can you help Smart compute this value?

Input Format

The input file contains a single line with two positive integers \( X \) and \( Y \) (where \( X < Y \)), representing the range for which the sum \( f(X) + f(X+1) + \ldots + f(Y) \) needs to be calculated.

Output Format

The output should be a single line containing the value of \( f(X) + f(X+1) + \ldots + f(Y) \).

Sample Input and Output

Sample Input #1

2 4

Sample Output #1

14

Sample Input #2

123 321

Sample Output #2

72543

Notes/Hints

• For 20% of the test cases, \( 1 \leq X < Y \leq 10^5 \).
• For 60% of the test cases, \( 1 \leq X < Y \leq 1 \times 10^7 \).
• For 100% of the test cases, \( 1 \leq X < Y \leq 2 \times 10^9 \).

见题面 Input 部分

见题面 Output 部分