F.java

package atcoder.arc.arc068;
 
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
 
public class Main {
    private static final int MOD = 1000000007;
 
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
 
        int n = in.nextInt();
        int k = in.nextInt();
        ncr = new int[2010][2010];
        for (int i = 0; i < ncr.length; i++) {
            ncr[i][0] = ncr[i][i] = 1;
            for (int j = 1 ; j < i; j++) {
                ncr[i][j] = (ncr[i-1][j] + ncr[i-1][j-1]);
                ncr[i][j] %= MOD;
            }
        }
 
        long ans = 0;
 
 
        // 次に処理する数,更新フラグ,保留数
        int[][][] dp = new int[2][2][n+1];
        dp[n%2][0][0] = 1;
        for (int i = n ; i >= 1 ; i--) {
            int fr = i%2;
            int to = fr^1;
            for (int flg = 0; flg <= 1; flg++) {
                Arrays.fill(dp[to][flg], 0);
            }
 
            int haveProcessedNumbers = n - i;
            for (int flg = 0; flg <= 1; flg++) {
                for (int j = n ; j >= 0; j--) {
                    if (dp[fr][flg][j] == 0) {
                        continue;
                    }
                    int base = dp[fr][flg][j];
                    int currentlyInSequence =  haveProcessedNumbers - j;
                    if (currentlyInSequence == k-1) {
                        ans = addMOD(ans, dp[fr][flg][j]);
                        continue;
                    }
                    if (flg == 1 && j >= 1) {
                        dp[fr][flg][j-1] = addMOD(dp[fr][flg][j-1], base);
                    }
                    if (i == 1) {
                        continue;
                    }
                    dp[to][1][j] = addMOD(dp[to][1][j], base);
                    dp[to][0][j+1] = addMOD(dp[to][0][j+1], base);
                }
            }
        }
 
        for (int i = 0 ; i < n-k-1 ; i++) {
            ans *= 2;
            ans %= MOD;
        }
        out.println(ans);
        out.flush();
    }
 
    private static int addMOD(long x, long y) {
        long ret = x + y;
        return (int)(ret >= MOD ? ret-MOD : ret);
    }
 
    static int[][] ncr;
 
    static long comb(int n, int k) {
        if (n < 0 || k < 0 || n < k) {
            return 0;
        }
        return ncr[n][k] % MOD;
    }
 
    // (以下テンプレにつき略)
}