One day Petya was solving a very interesting problem. But although he used many optimization techniques, his solution still got Time limit exceeded verdict. Petya conducted a thorough analysis of his program and found out that his function for finding maximum element in an array of *n* positive integers was too slow. Desperate, Petya decided to use a somewhat unexpected optimization using parameter *k*, so now his function contains the following code:

That way the function iteratively checks array elements, storing the intermediate maximum, and if after *k* consecutive iterations that maximum has not changed, it is returned as the answer.

Now Petya is interested in fault rate of his function. He asked you to find the number of permutations of integers from 1 to *n* such that the return value of his function on those permutations is not equal to *n*. Since this number could be very big, output the answer modulo 10<sup class="upper-index">9</sup> + 7.
The only line contains two integers *n* and *k* (1 ≤ *n*, *k* ≤ 10<sup class="upper-index">6</sup>), separated by a space — the length of the permutations and the parameter *k*.
Permutations from second example: 

[4, 1, 2, 3, 5], [4, 1, 3, 2, 5], [4, 2, 1, 3, 5], [4, 2, 3, 1, 5], [4, 3, 1, 2, 5], [4, 3, 2, 1, 5].
5 2
22
5 3
6
6 3
84
5 10
0
1 1
0
2 1
0
2 2
0
3 1
1
3 2
0
3 3
0
4 1
8
4 2
2
4 3
0
4 4
0
5 1
55
5 4
0
5 5
0
1000000 500000
900097839
1000000 1000000
0
1000000 1
131797017
1 1000000
0
959139 199252
770937198
9859 748096
0
125987 264237
0
209411 813081
0
325539 329221
0
376259 910770
0
492387 235422
249147139
608515 751563
0
691939 300407
700547157
30518 196518
0
146646 521171
0
230070 37311
993306535
313494 586155
0
396918 167704
943821934
513046 683844
0
629174 232688
831745227
679894 524637
655418678
796022 73481
883548575
879446 655030
563982505
405440 588704
0
from math import factorial

n, k = map(int, input().split())
res = 0
for a in range(k+1, n):
    for pos in range(0, a-k):
        q = factorial(a-1)*factorial(n-pos-k-1)//factorial(a-1-pos-k)
        res += q
print(res)
