Sherry likes matrices a lot, but her favorite ones are humble matrices. An matrix (we'll call it ) is humble if:
- It contains all the elements in range exactly once.
- For any elements and in matrix :
If , then should hold.
Given and , find and print the total number of possible humble matrices; as this number can be quite large, print your answer modulo .
Input Format
Two space-separated integers, and , respectively.
Constraints
Scoring
- for of the test data.
- for of the test data.
Output Format
Print the total number of humble matrices possible, modulo .
Sample Input 0
2 2
Sample Output 0
2
Sample Input 1
3 2
Sample Output 1
4
Explanation
There are possible humble matrices:
- [ 1, 2 ]
[ 3, 4 ] - [ 1, 3 ]
[ 2, 4 ]
Thus, we print the result of , which is .