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. <image> — 2 positions
  3. <image> — 2 positions
  4. <image> — 2 positions
  5. <image> — 2 positions
  6. (3, 2, 1) — 0 positions
import java.io.*;
import java.util.*;
public class E {
	
	long MOD = 1000000007;
	
    public void solve() throws IOException {
    	int n = nextInt();
    	int k = nextInt();
    	long[][] c = new long[n + 1][n + 1];
    	c[0][0] = 1;
    	for (int i = 1; i <= n; i++) {
    		c[i][0] = 1;
    		for (int j = 1; j <= i; j++)
    			c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % MOD; 
    	}
    	long[] fact = new long[n + 1];
    	fact[0] = 1;
    	for (int i = 1; i <= n; i++)
    		fact[i] = (fact[i - 1] * i) % MOD;
    	long[][][][] f = new long[n + 1][n + 1][2][2];
    	f[1][0][0][0] = 1;
    	f[1][1][0][1] = 1;
    	for (int i = 1; i < n; i++)
    		for (int j = 0; j <= i; j++)
    			for (int cur = 0; cur < 2; cur++)
    				for (int nex = 0; nex < 2; nex++) {
    					long value = f[i][j][cur][nex];
    					// nothing
    					f[i + 1][j][nex][0] = (f[i + 1][j][nex][0] + value) % MOD;
    					// take i 
    					if (cur == 0) f[i + 1][j + 1][nex][0] = (f[i + 1][j + 1][nex][0] + value) % MOD;
    					// take i + 2
    					if (i + 2 <= n) f[i + 1][j + 1][nex][1] = (f[i + 1][j + 1][nex][1] + value) % MOD;
    				}
    	long[] tot = new long[n + 1];
    	for (int j = 0; j <= n; j++)
    		for (int cur = 0; cur < 2; cur++)
    			tot[j] = (tot[j] + f[n][j][cur][0]) % MOD;
    	//for (int i = 0; i <= n; i++) writer.print(tot[i] + " ");
    	//writer.println();
    	for (int i = n; i >= 0; i--) {
    		tot[i] = (tot[i] * fact[n - i]) % MOD;
    		//writer.println(i + " " + tot[i]);
    		for (int j = i + 1; j <= n; j++) {
    			long sub = (tot[j] * c[j][i]) % MOD;
    			tot[i] = (tot[i] - sub + MOD) % MOD;
    		}
    	}
    	writer.println(tot[k]);
    }
    
    public static void main(String[] args) throws FileNotFoundException {
        new E().run();
    }

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter writer;

    public void run() {
        try {
            long tbegin = System.currentTimeMillis();
            reader = new BufferedReader(new InputStreamReader(System.in));
            //reader = new BufferedReader(new InputStreamReader(new FileInputStream("art.in")));
            tokenizer = null;
            writer = new PrintWriter(System.out);
            //writer = new PrintWriter(new FileOutputStream("art.out"));
            solve();
            //reader.close();
            //System.out.println(System.currentTimeMillis() - tbegin + "ms");
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    String nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

}