You are given a grid, consisting of 2 rows and n columns. Each cell of this grid should be colored either black or white.

Two cells are considered neighbours if they have a common border and share the same color. Two cells A and B belong to the same component if they are neighbours, or if there is a neighbour of A that belongs to the same component with B.

Let's call some bicoloring beautiful if it has exactly k components.

Count the number of beautiful bicolorings. The number can be big enough, so print the answer modulo 998244353.

Input

The only line contains two integers n and k (1 ≤ n ≤ 1000, 1 ≤ k ≤ 2n) — the number of columns in a grid and the number of components required.

Output

Print a single integer — the number of beautiful bicolorings modulo 998244353.

Examples

Input

3 4


Output

12


Input

4 1


Output

2


Input

1 2


Output

2

Note

One of possible bicolorings in sample 1:

<image>
import java.io.*;
import java.util.*;

public class P1051D {
    static String probName = "template";
    static Comparator<int[]> comp = new Comparator<int[]>() {
        public int compare(int[] a, int[] b) {
            for (int i=0; i<a.length; i++) {
                if (a[i] < b[i])       return -1;
                else if (a[i] > b[i])  return 1;
            }
            return 0;
        }
    };
    static final long LARGE_LONG = 1000000000000000000L;
    static final int LARGE_INT = 1000000007;
    static final int MOD_INT = 998244353;
    static final int[] dx = new int[] {1, -1, 0, 0};
    static final int[] dy = new int[] {0, 0, 1, -1};
    static int n;
    static int k;
    static long[][][] table;

    public static void main(String[] argst) throws IOException {
        FastReader in = new FastReader();
        // FastReader in = new FastReader(probName + ".in");
        // Scanner in = new Scanner(System.in);

        // PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter(probName + ".out")));
        PrintWriter out = new PrintWriter(System.out);
        //out.println("Hi");
        //out.flush();
        n = in.nextInt();
        k = in.nextInt();
        table = new long[n+1][k+2][4];
        table[1][1][0] = 1;
        table[1][2][1] = 1;
        table[1][2][2] = 1;
        table[1][1][3] = 1;
        long tot = 0;
        //out.println(n + " " + k);
        //out.flush();
        for (int i = 2; i <= n; i++) {
            table[i][1][0] = table[i-1][1][0] + table[i-1][1][1] + table[i-1][1][2] + table[i-1][0][3];
            table[i][1][1] = table[i-1][0][0] + table[i-1][1][1] + table[i-1][0][3];
            table[i][1][2] = table[i-1][0][0] + table[i-1][1][2] + table[i-1][0][3];
            table[i][1][3] = table[i-1][0][0] + table[i-1][1][1] + table[i-1][1][2] + table[i-1][1][3];
            for (int j = 2; j <= k; j++) {
                table[i][j][0] = (table[i-1][j][0] + table[i-1][j][1] + table[i-1][j][2] + table[i-1][j-1][3])%MOD_INT;
                table[i][j][1] = (table[i-1][j-1][0] + table[i-1][j][1] + table[i-1][j-2][2] + table[i-1][j-1][3])%MOD_INT;
                table[i][j][2] = (table[i-1][j-1][0] + table[i-1][j-2][1] + table[i-1][j][2] + table[i-1][j-1][3])%MOD_INT;
                table[i][j][3] = (table[i-1][j-1][0] + table[i-1][j][1] + table[i-1][j][2] + table[i-1][j][3])%MOD_INT;
            }
        }
        tot += table[n][k][0];
        tot += table[n][k][1];
        tot += table[n][k][2];
        tot += table[n][k][3];
        out.println(tot%MOD_INT);
        out.close();
    }

    /* FastReader code from  https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/
       nextLine modified, and added next(), and hasNext()
    */

    static class FastReader {
        final private int BUFFER_SIZE = 1 << 16;
        final private int MAX_LINE_SIZE = 1 << 20;
        private DataInputStream din;
        private byte[] buffer, lineBuf;
        private int bufferPointer, bytesRead;

        public FastReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
        public FastReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
        public boolean hasNext() throws IOException {
            byte c;
            while ((c = read()) != -1) {
                if (c > ' ') {
                    bufferPointer--;
                    return true;
                }
            }
            return false;
        }
        public String nextLine() throws IOException {
            if (lineBuf == null)	lineBuf = new byte[MAX_LINE_SIZE];
            int ctr = 0;
            byte c;
            while ((c = read()) != -1) {
                if (c == '\r')        continue;
                if (c == '\n')        break;
                lineBuf[ctr++] = c;
            }
            return new String(lineBuf, 0, ctr);
        }
        public String next() throws IOException {
            if (lineBuf == null)	lineBuf = new byte[MAX_LINE_SIZE];
            int ctr = 0;
            byte c = read();
            while (c <= ' ')  	c = read();
            while (c > ' ') {
                lineBuf[ctr++] = c;
                c = read();
            }
            return new String(lineBuf, 0, ctr);
        }
        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')   c = read();
            boolean neg = (c == '-');
            if (neg)           c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)           return -ret;
            return ret;
        }
        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')    c = read();
            boolean neg = (c == '-');
            if (neg)            c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)            return -ret;
            return ret;
        }
        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)  	c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }
            if (neg)     return -ret;
            return ret;
        }
        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
        private byte read() throws IOException {
            if (bufferPointer == bytesRead)     fillBuffer();
            return buffer[bufferPointer++];
        }
        public void close() throws IOException {
            if (din == null) 	   return;
            din.close();
        }
    }
}

