Reconciled?

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.

Examples

Input

2 2

Output

8

Input

3 2

Output

12

Input

1 8

Output

0

Input

100000 100000

Output

530123477

inputFormat

Input

Input is given from Standard Input in the following format:

N M

outputFormat

Output

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

Examples

Input

2 2

Output

8

Input

3 2

Output

12

Input

1 8

Output

0

Input

100000 100000

Output

530123477

样例

100000 100000

530123477