Problem3520--Positions in Permutations

3520: Positions in Permutations

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Permutation p is an ordered set of integers p1,p2,...,pn, consisting of n distinct positive integers, each of them doesn't exceed n. We'll denote the i-th element of permutation p as pi. We'll call number n the size or the length of permutation p1,p2,...,pn.

We'll call position i (1≤i≤n) in permutation p1,p2,...,pn good, if |p[i]-i|=1. Count the number of permutations of size n with exactly k good positions. Print the answer modulo 1000000007 (109+7).

Input

The single line contains two space-separated integers n and k (1≤n≤1000,0≤k≤n).

Output

Print the number of permutations of length n with exactly k good positions modulo 1000000007 (109+7).

Examples
Input
1 0
Output
1
Input
2 1
Output
0
Input
3 2
Output
4
Input
4 1
Output
6
Input
7 4
Output
328
Note

The only permutation of size 1 has 0 good positions.

Permutation (1,2) has 0 good positions, and permutation (2,1) has 2 positions.

Permutations of size 3:

  1. (1,2,3) − 0 positions
  2. − 2 positions
  3. − 2 positions
  4. − 2 positions
  5. − 2 positions
  6. (3,2,1) − 0 positions

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