Strange Metro Rail
Description
There is a strange metro rail that starts from station $L$ and its destination station is $R$. The rail has only one entry door and one exit door. People can enter the rail from any station but they can only get off the rail at the destination station $R$.
Rail will stop at every station from $L$ to $R$. For a particular station $K$, Rail will stop for $LCM(K, R)$ minutes and it takes $K$ minutes for a person to get into the train. The door is so narrow that no two people can enter the rail at the same time.
Can you calculate the maximum number of possible persons at the destination station $R$? Since the answer can be very large, print it modulo $10^9+7$.
The input contains two positive integer numbers in the first line: $L, R$ $(1 \leq L \leq R \leq 10^{12})$.
Print a single integer number — maximum number of possible persons at the destination station $R$.
Input
The input contains two positive integer numbers in the first line: $L, R$ $(1 \leq L \leq R \leq 10^{12})$.
Output
Print a single integer number — maximum number of possible persons at the destination station $R$.
6 10
31
Note
At station $6$: Rail stops for $LCM(6,10)=30$min. $5$ persons can enter.
At station $7$: Rail stops for $LCM(7,10)=70$min. $10$ persons can enter.
At station $8$: Rail stops for $LCM(8,10)=40$min. $5$ persons can enter.
At station $9$: Rail stops for $LCM(9,10)=90$min. $10$ persons can enter.
At station $10$: Rail stops for $LCM(10,10)=10$min. $1$ person can enter.
Maximum $(5+10+5+10+1)=31$ people can be at the destination station $10$.