Problem: 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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;
const int mod = 924844033;
const int maxn = 4000 + 10;
typedef long long int lli;

int link[maxn];
lli x[maxn];
lli dp[maxn][maxn][2];

int main() {
    int n, k, tot = 0;
    scanf("%d%d", &n, &k);
    for (int i = 1; i <= k; i++) {//i枚举链的起点
        for (int p = 0; p < 2; p++) {//因为p=0时,起点为第i个点,p=1时,为第i个坑
            for (int j = i; j <= n; j += k) {
                tot++;
                if (j != i) link[tot] = 1;//link[i]代表第i条边是否与上一条边相连
            }
        }
    }
    x[1] = 1;
    x[0] = 1;
    for (int i = 2; i <= n; i++) {
        x[i] = x[i - 1] * i % mod;
    }
    dp[0][0][0] = 1;
    for (int i = 0; i < n * 2; i++) {
        for (int j = 0; j <= n; j++) {
            dp[i + 1][j][0] = (dp[i][j][0] + dp[i][j][1]) % mod;
            if (link[i + 1]) dp[i + 1][j + 1][1] = dp[i][j][0];
        }
    }
    lli sum = 0, t = 1;
    for (int i = 0; i <= n; i++) {
        lli tmp = (dp[n * 2][i][0] + dp[n * 2][i][1]) % mod * x[n - i] % mod;
        sum = (sum + (tmp * t + mod) % mod) % mod;
        t *= -1;
    }
    printf("%lld\n", sum);
    return 0;
}