There are $n$ male students, $m$ female students, and two teachers in a middle school who need to line up for a physical examination. They form a single line such that no two female students are adjacent, and the two teachers are also not adjacent. How many possible arrangements are there? (Note: Every individual is distinct.)

Input

The input consists of a single line containing two non-negative integers $n$ and $m$, separated by a space, with the meanings as described above.

Constraints

• For 30% of the data: $n \le 100, m \le 100$
• For 100% of the data: $n \le 2000, m \le 2000$

Output

The output should contain a single non-negative integer representing the number of different arrangements. Note that the answer may be very large.

Examples

Input 1

1 1

Output 1

12

Input 2

7 3

Output 2

220631040