~K Perm Counting

Snuke loves permutations. He is making a permutation of length N.

Since he hates the integer K, his permutation will satisfy the following:

• Let the permutation be a_1, a_2, ..., a_N. For each i = 1,2,...,N, |a_i - i| \neq K.

Among the N! permutations of length N, how many satisfies this condition?

Since the answer may be extremely large, find the answer modulo 924844033(prime).

Constraints

• 2 ≦ N ≦ 2000
• 1 ≦ K ≦ N-1

Input

The input is given from Standard Input in the following format:

N K

Output

Print the answer modulo 924844033.

Examples

Input

3 1

Output

2

Input

4 1

Output

5

Input

4 2

Output

9

Input

4 3

Output

14

Input

425 48

Output

756765083

inputFormat

Input

The input is given from Standard Input in the following format:

N K

outputFormat

Output

Print the answer modulo 924844033.

Examples

Input

3 1

Output

2

Input

4 1

Output

5

Input

4 2

Output

9

Input

4 3

Output

14

Input

425 48

Output

756765083

样例

425 48

756765083