100652: [AtCoder]ABC065 C - Reconciled?

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

Score : $300$ points

Problem Statement

Snuke has $N$ dogs and $M$ monkeys. He wants them to line up in a row.

As a Japanese saying goes, these dogs and monkeys are on bad terms. ("ken'en no naka", literally "the relationship of dogs and monkeys", means a relationship of mutual hatred.) Snuke is trying to reconsile them, by arranging the animals so that there are neither two adjacent dogs nor two adjacent monkeys.

How many such arrangements there are? Find the count modulo $10^9+7$ (since animals cannot understand numbers larger than that). Here, dogs and monkeys are both distinguishable. Also, two arrangements that result from reversing each other are distinguished.

Constraints

  • $1 ≤ N,M ≤ 10^5$

Input

Input is given from Standard Input in the following format:

$N$ $M$

Output

Print the number of possible arrangements, modulo $10^9+7$.


Sample Input 1

2 2

Sample Output 1

8

We will denote the dogs by A and B, and the monkeys by C and D. There are eight possible arrangements: ACBD, ADBC, BCAD, BDAC, CADB, CBDA, DACB and DBCA.


Sample Input 2

3 2

Sample Output 2

12

Sample Input 3

1 8

Sample Output 3

0

Sample Input 4

100000 100000

Sample Output 4

530123477

Input

题意翻译

## 题目描述 すぬけ君养了 $ N $ 只狗和 $M$ 只猴。すぬけ君想把这 $N+M$ 只动物排成一列。 すぬけ君希望狗与狗不能互相挨着,猴与猴不能互相挨着。 这样的排列方式有多少种?请输出答案对 $10^9+7$ 取模的结果。不过,狗与狗间,猴与猴间相互区别。 ## 数据范围 - $1 \leq N,M \leq 10^5 $ ## 输入 输入按以下标准: ``` N M ``` ## 输出 输出方案数对 $10^9+7$ 取模的结果 ## 样例1解释 将每只狗分别记为`A`,`B`,将每只猴分别记为`C`,`D`,则共有`ACBD`,`ADBC`,`BCAD`,`BDAC`,`CADB`,`CBDA`,`DACB`,`DBCA` $8$ 种排列方法。 感谢@ミク 提供的翻译

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