Snuke has decided to play with N cards and a deque (that is, a double-ended queue). Each card shows an integer from 1 through N, and the deque is initially empty.

Snuke will insert the cards at the beginning or the end of the deque one at a time, in order from 1 to N. Then, he will perform the following action N times: take out the card from the beginning or the end of the deque and eat it.

Afterwards, we will construct an integer sequence by arranging the integers written on the eaten cards, in the order they are eaten. Among the sequences that can be obtained in this way, find the number of the sequences such that the K-th element is 1. Print the answer modulo 10^{9} + 7.

Constraints

* 1 ≦ K ≦ N ≦ 2{,}000

Input

The input is given from Standard Input in the following format:


N K


Output

Print the answer modulo 10^{9} + 7.

Examples

Input

2 1


Output

1


Input

17 2


Output

262144


Input

2000 1000


Output

674286644
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Egor Kulikov (egor@egork.net)
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskF solver = new TaskF();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskF {
        long[][] answer;
        long[][] sum;
        int base;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            int k = in.readInt();
            base = n - k + 1;
            answer = new long[n + 1][n + 1];
            sum = new long[n + 1][n + 1];
            ArrayUtils.fill(answer, -1);
            ArrayUtils.fill(sum, -1);
            long answer = go(n, n) * IntegerUtils.power(2, Math.max(n - k - 1, 0), MiscUtils.MOD7) % MiscUtils.MOD7;
            out.printLine(answer);
        }

        private long go(int n, int lim) {
            lim = Math.min(lim, n);
            if (answer[n][lim] != -1) {
                return answer[n][lim];
            }
            if (n == base) {
                return answer[n][lim] = 1;
            }
            return answer[n][lim] = (go(n - 1, lim) + goSum(n - 1, lim - 1)) % MiscUtils.MOD7;
        }

        private long goSum(int n, int lim) {
            if (sum[n][lim] != -1) {
                return sum[n][lim];
            }
            if (lim <= 1) {
                return sum[n][lim] = 0;
            }
            return sum[n][lim] = (go(n, lim) + goSum(n, lim - 1)) % MiscUtils.MOD7;
        }

    }

    static class ArrayUtils {
        public static void fill(long[][] array, long value) {
            for (long[] row : array) {
                Arrays.fill(row, value);
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }

    }

    static class IntegerUtils {
        public static long power(long base, long exponent, long mod) {
            if (base >= mod) {
                base %= mod;
            }
            if (exponent == 0) {
                return 1 % mod;
            }
            long result = power(base, exponent >> 1, mod);
            result = result * result % mod;
            if ((exponent & 1) != 0) {
                result = result * base % mod;
            }
            return result;
        }

    }

    static class MiscUtils {
        public static final int MOD7 = (int) (1e9 + 7);

    }
}

