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
//package round175;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class E2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), K = ni();
		int mod = 1000000007;
		long[][][][] dp = new long[n][n+1][2][2];
		dp[0][0][0][0] = 1;
		for(int i = 1;i < n;i++){
			for(int j = 0;j <= n;j++){
				dp[i][j][0][0] += dp[i-1][j][0][0];
				dp[i][j][0][0] += dp[i-1][j][0][1];
				dp[i][j][0][0] += dp[i-1][j][1][0];
				dp[i][j][0][0] += dp[i-1][j][1][1];
				dp[i][j][0][0] %= mod;
				if(j-1 >= 0){
					dp[i][j][0][1] += dp[i-1][j-1][0][0];
					dp[i][j][0][1] += dp[i-1][j-1][0][1];
					dp[i][j][1][0] += dp[i-1][j-1][0][0];
					dp[i][j][1][0] += dp[i-1][j-1][1][0];
					dp[i][j][0][1] %= mod;
					dp[i][j][1][0] %= mod;
				}
				if(j-2 >= 0){
					dp[i][j][1][1] += dp[i-1][j-2][0][0];
				}
			}
		}
		
		int[][] fif = enumFIF(n, mod);
		
		long[] F = new long[n+1];
		for(int j = 0;j <= n;j++){
			for(int k = 0;k < 2;k++){
				for(int l = 0;l < 2;l++){
					F[j] += dp[n-1][j][k][l];
				}
			}
			F[j] %= mod;
		}
		
		long ret = 0;
		for(int j = K;j <= n;j++){
			long plus = F[j] * fif[0][n-j] % mod * fif[0][j]%mod*fif[1][j-K]%mod*fif[1][K]%mod;
			if((K-j)%2 == 0){
				ret += plus;
			}else{
				ret += mod-plus;
			}
		}
		out.println(ret%mod);
	}
	
	public static int[][] enumFIF(int n, int mod)
	{
		int[] f = new int[n+1];
		int[] invf = new int[n+1];
		invf[1] = 1;
		for(int i = 2;i <= n;i++){
			invf[i] = (int)(invf[mod%i]*(long)(mod-mod/i)%mod);
		}
		
		f[0] = invf[0] = 1;
		for(int i = 1;i <= n;i++){
			f[i] = (int)((long)f[i-1] * i % mod);
			invf[i] = (int)((long)invf[i-1] * invf[i] % mod);
		}
		return new int[][]{f, invf};
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new E2().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}
