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Problems

Sigma-function on a segment

Sigma-function on a segment

Time limit 1 second
Memory limit 128 MiB

Find

prb2888.gif

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

Input data

Contains no more than 10^5 queries. Each query is given on a separate line and contains two numbers l and r (1lr5 * 10^6).

Output data

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

Examples

Input example #1
3 10
Output example #1
83
Source 2012 Kharkiv, Winter School, Day of Sergey Kopelovich, Problem H