Ayoub and Lost Array

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


2 1 3

输出样例 #1


3

输入样例 #2


3 2 2

输出样例 #2


1

输入样例 #3


9 9 99

输出样例 #3


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] $ .