A12289. Ayoub and Lost Array

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.

In the first example, the possible arrays are : $[1,2], [2,1], [3, 3]$ .

In the second example, the only possible array is $[2, 2, 2]$ .