# CF1105C Ayoub and Lost Array

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## 题意翻译

已知有一个长度为$n$($1\leq n\leq 2 \times 10^5$)的数列，每一个数的大小在$[l,r]$($1\leq l \leq r \leq 10^9$)之间。求出有多少种方案使得这个数列的和为$3$的倍数。答案对$10^9+7$取模。当然，如果无法组成任何一个合法的数列，答案即为$0$。

## 输入格式

一行三个正整数$n$,$l$,$r$

## 输出格式

一行，表示方案数模$10^9+7$的结果。

## 题目描述

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 $0$ .

## 输入输出格式

输入格式：

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.

输出格式：

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

## 输入输出样例

输入样例#1： 复制
2 1 3

输出样例#1： 复制
3

输入样例#2： 复制
3 2 2

输出样例#2： 复制
1

输入样例#3： 复制
9 9 99

输出样例#3： 复制
711426616


## 说明

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

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

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