Ayoub and Lost Array
Description
Ayoub had an array $a$ of integers of size $n$ and this array had two interesting properties:
- All the integers in the array were between $l$ and $r$ (inclusive).
- The sum of all the elements was divisible by $3$.
Unfortunately, Ayoub has lost his array, but he remembers the size of the array $n$ and the numbers $l$ and $r$, so he asked you to find the number of ways to restore the array.
Since the answer could be very large, print it modulo $10^9 + 7$ (i.e. the remainder when dividing by $10^9 + 7$). In case there are no satisfying arrays (Ayoub has a wrong memory), print $0$.
The first and only line contains three integers $n$, $l$ and $r$ ($1 \le n \le 2 \cdot 10^5 , 1 \le l \le r \le 10^9$) — the size of the lost array and the range of numbers in the array.
Print the remainder when dividing by $10^9 + 7$ the number of ways to restore the array.
Input
The first and only line contains three integers $n$, $l$ and $r$ ($1 \le n \le 2 \cdot 10^5 , 1 \le l \le r \le 10^9$) — the size of the lost array and the range of numbers in the array.
Output
Print the remainder when dividing by $10^9 + 7$ the number of ways to restore the array.
Samples
2 1 3
3
3 2 2
1
9 9 99
711426616
Note
In the first example, the possible arrays are : $[1,2], [2,1], [3, 3]$.
In the second example, the only possible array is $[2, 2, 2]$.