Kelia is a wealthy girl. After growing up, she started her own business and opened a company. However, managing a company is exhausting work. Employees often slack off behind Kelia's back, so she needs to inspect the offices from time to time.

Kelia's company has $n$ offices, numbered from $l$ to $l+n-1$. Kelia predetermines an order and inspects the offices one by one according to this sequence. Initially, all employees are slacking off. When she finishes inspecting the office with number $i$, the employees in that office start working diligently, and they notify all offices with numbers that are multiples of $i$ that the boss has arrived, telling them to work diligently. Therefore, when Kelia finishes inspecting the $i$-th office, the employees in all offices with numbers that are multiples of $i$ (including $i$ itself) will start working diligently.

Kelia discovered this behavior of the employees tipping each other off. She found that for every different permutation $p$, there exists a minimum $t(p)$ such that after Kelia finishes inspecting the first $t(p)$ offices in this order, all offices start working diligently. She defines this $t(p)$ as the inspection time of $p$.

Kelia wants to know the sum of all $t(p)$.

Since this result might be very large, she wants to know the sum modulo $10^9+7$.

Input

The first line contains two integers $l$ and $r$ representing the range of office numbers, where $n = r-l+1$.

Output

A single integer representing the sum of all $t(p)$ modulo $10^9+7$.

Examples

Input 1

2 4

Output 1

16

Note 1

Consider all relative orders of office inspections:

• 2 3 4, time is $2$.
• 3 2 4, time is $2$.
• 4 2 3, time is $3$.
• 4 3 2, time is $3$.
• 2 4 3, time is $3$.
• 3 4 2, time is $3$.

The sum is $16$.

Input 2

4 12

Output 2

3110400

Subtasks

For $20\%$ of the data, $r-l+1 \leq 8$.

For another $10\%$ of the data, $l=1$.

For another $10\%$ of the data, $l=2$.

For another $30\%$ of the data, $l \leq 200$.

For $100\%$ of the data, $1 \leq l \leq r \leq 10^7$.