3469. Savrsen

A number is perfect if it is equal to the sum of its divisors, the ones that are smaller than it. For example, number $28$ is perfect because $28 = 1 + 2 + 4 + 7 + 14$.

Motivated by this definition, we introduce the metric of imperfection of number $N$, denoted with $f(N)$, as the absolute difference between $N$ and the sum of its divisors less than $N$. It follows that perfect numbers’ imperfection score is $0$, and the rest of natural numbers have a higher imperfection score. For example:

• $f(6) = |6 - 1 - 2 - 3| = 0$,
• $f(11) = |11 - 1| = 10$,
• $f(24) = |24 - 1 - 2 - 3 - 4 - 6 - 8 - 12| = |-12| = 12$.

Write a programme that, for positive integers $A$ and $B$, calculates the sum of imperfections of all numbers between $A$ and $B$: $f(A) + f(A + 1) + \ldots + f(B)$.

输入

The first line of input contains the positive integers $A$ and $B$ ($1 \le A \le B \le 10^7$).

输出

The first and only line of output must contain the required sum.

样例

Input
24 24

Output
12

Input
1 9

Output
21


提示

Clarification of the first test case: $1 + 1 + 2 + 1 + 4 + 0 + 6 + 1 + 5$.

25 人解决，35 已尝试。

50 份提交通过，共有 146 份提交。

8.1 EMB 奖励。