CF1105C.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 $0$.

Ayoub 原本有一个长度为 $n$ 的整数数组 $a$，该数组具有以下两个有趣的性质：

• 数组中所有整数均在 $l$ 和 $r$ 之间（含端点）；
• 所有元素之和能被 $3$ 整除。

不幸的是，Ayoub 弄丢了这个数组，但他还记得数组的长度 $n$ 以及数值 $l$ 和 $r$，因此他请你帮忙计算出恢复该数组的方案数。

由于答案可能非常大，请输出其对 $10^9 + 7$ 取模的结果（即除以 $10^9 + 7$ 后的余数）。如果不存在满足条件的数组（即 Ayoub 记错了），请输出 $0$。

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.

第一行且唯一一行包含三个整数 $n$、$l$ 和 $r$（$1 \le n \le 2 \cdot 10^5$，$1 \le l \le r \le 10^9$）—— 分别表示丢失数组的大小以及数组中数字的取值范围。

Print the remainder when dividing by $10^9 + 7$ the number of ways to restore the array.

输出将数组恢复原状的方案数对 $10^9 + 7$ 取模后的余数。

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

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

在第一个例子中，可能的数组有：$[1,2], [2,1], [3, 3]$。

在第二个例子中，唯一可能的数组是 $[2, 2, 2]$。