Sigma-function on a segment

Find

where σ(i) is the sum of positive divisors of number i.

Input

Contains no more than 10^5 queries. Each query is given on a separate line and contains two numbers l and r (1 ≤ l ≤ r ≤ 5 * 10^6).

Output

For each query print on a separate line one number S(l, r).

Examples