288_B. Polo the Penguin and Houses 
Little penguin Polo loves his home village. The village has n houses, indexed by integers from 1 to n. Each house has a plaque containing an integer, the i-th house has a plaque containing integer pi (1 ≤ pi ≤ n).

Little penguin Polo loves walking around this village. The walk looks like that. First he stands by a house number x. Then he goes to the house whose number is written on the plaque of house x (that is, to house px), then he goes to the house whose number is written on the plaque of house px (that is, to house ppx), and so on.

We know that:

  1. When the penguin starts walking from any house indexed from 1 to k, inclusive, he can walk to house number 1. 
  2. When the penguin starts walking from any house indexed from k + 1 to n, inclusive, he definitely cannot walk to house number 1. 
  3. When the penguin starts walking from house number 1, he can get back to house number 1 after some non-zero number of walks from a house to a house. 



You need to find the number of ways you may write the numbers on the houses' plaques so as to fulfill the three above described conditions. Print the remainder after dividing this number by 1000000007 (109 + 7).

Input

The single line contains two space-separated integers n and k (1 ≤ n ≤ 1000, 1 ≤ k ≤ min(8, n)) — the number of the houses and the number k from the statement.

Output

In a single line print a single integer — the answer to the problem modulo 1000000007 (109 + 7).

Examples

Input

5 2


Output

54


Input

7 4


Output

1728
```python
import sys,math,heapq,copy
from collections import defaultdict,deque
from bisect import bisect_left,bisect_right
from functools import cmp_to_key
from itertools import permutations,combinations,combinations_with_replacement
# sys.setrecursionlimit(10**6)
# sys.stdin=open('Input.txt','r')
# sys.stdout=open('Output.txt','w')
mod=1000000007
# Reading Single Input
def get_int(): return int(sys.stdin.readline().strip())
def get_str(): return sys.stdin.readline().strip()
def get_float(): return float(sys.stdin.readline().strip())
# Reading Multiple Inputs
def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_strs(): return map(str, sys.stdin.readline().strip().split())
def get_floats(): return map(float, sys.stdin.readline().strip().split())
# Reading List Of Inputs
def list_ints(): return list(map(int, sys.stdin.readline().strip().split()))
def list_strs(): return list(map(str, sys.stdin.readline().strip().split()))
def list_floats(): return list(map(float, sys.stdin.readline().strip().split()))
# ------------------------------------------------------------------------------------- #

n,k=get_ints()
print((pow(k,k-1,mod)*pow(n-k,n-k,mod))%mod)
```