100652: [AtCoder]ABC065 C - Reconciled?
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