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.*;
import java.math.*;
import java.lang.*;

public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        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 String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int nextInt() {
            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 long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long 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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

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

    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(), "Main", 1 << 27).start();
    }

    static class Pair {
        int f;
        int s;
        int p;
        PrintWriter w;

        // int t;

        Pair(int f, int s) {
            // Pair(int f,int s, PrintWriter w){
            this.f = f;
            this.s = s;
            // this.p = p;
            // this.w = w;
            // this.t = t;

        }

        public static Comparator<Pair> wc = new Comparator<Pair>() {
            public int compare(Pair e1,Pair e2){

                // 1 for swap
                if(Math.abs(e1.f)-Math.abs(e2.f)!=0){
                    // e1.w.println("**"+e1.f+" "+e2.f);
                    return (Math.abs(e1.f)-Math.abs(e2.f));
                }
                else{
                    // e1.w.println("##"+e1.f+" "+e2.f);
                    return (Math.abs(e1.s)-Math.abs(e2.s));
                }


            }
        };
    }

    public Integer[] sort(Integer[] a) {
        Arrays.sort(a);
        return a;
    }

    public Long[] sort(Long[] a) {
        Arrays.sort(a);
        return a;
    }

    public static ArrayList<Integer> sieve(int N) {
        int i, j, flag;

        ArrayList<Integer> p = new ArrayList<Integer>();

        for (i = 1; i < N; i++) {

            if (i == 1 || i == 0)
                continue;

            flag = 1;

            for (j = 2; j <= i / 2; ++j) {
                if (i % j == 0) {
                    flag = 0;
                    break;
                }
            }
            if (flag == 1) {
                p.add(i);
            }
        }
        return p;
    }

    public static long gcd(long a, long b) {
        if (b == 0)
            return a;
        else
            return gcd(b, a % b);
    }

    public static int gcd(int a, int b) {
        if (b == 0)
            return a;
        else
            return gcd(b, a % b);
    }

    //// recursive dfs
    public static int dfs(int s, ArrayList<Integer>[] g, long[] dist, boolean[] v, PrintWriter w, int p) {
        v[s] = true;
        int ans = 1;
        // int n = dist.length - 1;
        int t = g[s].size();
        // int max = 1;
        for (int i = 0; i < t; i++) {
            int x = g[s].get(i);
            if (!v[x]) {
                // dist[x] = dist[s] + 1;
                ans = Math.min(ans, dfs(x, g, dist, v, w, s));
            } else if (x != p) {
                // w.println("* " + s + " " + x + " " + p);
                ans = 0;
            }
        }
        // max = Math.max(max,(n-p));
        return ans;
    }

    //// iterative BFS
    public static int bfs(int s, ArrayList<Integer>[] g, long[] dist, boolean[] b, PrintWriter w, int p) {
        b[s] = true;
        int siz = 1;
        // dist--;
        Queue<Integer> q = new LinkedList<>();
        q.add(s);
        while (q.size() != 0) {
            int i = q.poll();
            Iterator<Integer> it = g[i].listIterator();
            int z = 0;
            while (it.hasNext()) {
                z = it.next();
                if (!b[z]) {
                    b[z] = true;
                    // dist--;
                    dist[z] = dist[i] + 1;
                    // siz++;
                    q.add(z);
                } else if (z != p) {
                    siz = 0;
                }
            }

        }
        return siz;
    }

    public static int lower(int a[], int x) { // x is the target value or key
        int l = -1, r = a.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] >= x)
                r = m;
            else
                l = m;
        }
        return r;
    }

    public static int upper(int a[], int x) {// x is the key or target value
        int l = -1, r = a.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] <= x)
                l = m;
            else
                r = m;
        }
        return l + 1;
    }

    public static int lower(ArrayList<Integer> a, int x) { // x is the target value or key
        int l = -1, r = a.size();
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a.get(m) >= x)
                r = m;
            else
                l = m;
        }
        return r;
    }

    public static int upper(ArrayList<Integer> a, int x) {// x is the key or target value
        int l = -1, r = a.size();
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a.get(m) <= x)
                l = m;
            else
                r = m;
        }
        return l + 1;
    }

    public static long power(long x, long y, long m) {
        if (y == 0)
            return 1;

        long p = power(x, y / 2, m) % m;
        p = (p * p) % m;

        if (y % 2 == 0)
            return p;
        else
            return (x * p) % m;
    }

    public void yesOrNo(boolean f) {
        if (f) {
            w.println("YES");
        } else {
            w.println("NO");
        }
    }

    // Arrays.sort(rooms, (room1, room2) -> room1[1] == room2[1] ? room1[0]-room2[0]
    // : room2[1]-room1[1]);
    // Arrays.sort(A, (a, b) -> Integer.compare(a[0] , b[0]));
    //////////////////////////////////////////////////////////////////////////////////////////////////////
    //////////////////////////////////////////////////////////////////////////////////////////////////////
    // code here
    int oo = (int) 1e9;
    int[] parent;
    int[] dist;
    int[] height;
    boolean[] vis;
    // ArrayList<Integer>[] g;
    // int[] col;
    // HashMap<Long, Boolean>[] dp;
    char[][] g;
    // boolean[][] v;
    // long[] a;
    // ArrayList<Integer[]> a;
    // int[][] ans;
    long[][][] dp;
    long mod;
    int n;
    int m;
    int k;
    long[][] pre;
    // StringBuilder[] a;
    // StringBuilder[] b;
    // StringBuilder ans;
    int[][] col;
    int[][] row;
    PrintWriter w = new PrintWriter(System.out);

    public void run() {

        InputReader sc = new InputReader(System.in);

        int defaultValue = 0;
        mod =  998244353;

        int test = 1;
        //test = sc.nextInt();
        //w.println("test="+test);
        while (test-- > 0) {
            n = sc.nextInt();
            k = sc.nextInt();
            dp = new long[n][k+1][4];

            for(int i=0;i<n;i++){
                for(int j=0;j<=k;j++){
                    Arrays.fill(dp[i][j],-1);
//                    Arrays.fill(dp[i][j][1],-1);
//                    Arrays.fill(dp[i][j][2],-1);
//                    Arrays.fill(dp[i][j][3],-1);
                }
            }

            long ans = 0;
            for(int i=0;i<4;i++){
                int newJ = add(i, i^3);
                ans = (ans+sol(1,newJ,i))%mod;
            }
            w.println(ans);
        }

        w.flush();
        w.close();

    }

    public long sol(int i, int j, int c){

        if(i>n || j>k)return 0;
        if(i==n){
            if(j==k)return 1;
            else return 0;
        }
        else if(dp[i][j][c]!=-1)return dp[i][j][c];
        else{
            long ans = 0;
            for(int z=0;z<4;z++){
                int newJ = j+add(z,c);
                ans = (ans+sol(i+1,newJ,z))%mod;
            }
            dp[i][j][c] = ans;
            return ans;
        }

    }

    public int add(int c, int d){
        if(d==0){
            if(c!=0) {
                return 1;
            }
            else{
                return 0;
            }
        }
        else if(d==1){
            if(c!=2) {
                return 0;
            }
            else{
                return 2;
            }
        }
        else if(d==2){
            if(c!=1) {
                return 0;
            }
            else{
                return 2;
            }
        }
        else{
            if(c!=3){
                return 1;
            }
            else{
                return 0;
            }
        }
    }

}
