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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
public class D {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	static int N,K;
	static int n, k;
	static long mod = 998244353; 
	static long dp[][][][];

	void solve()
	{	
		n = ni(); k = ni();
		// long mod = 998244353;
		dp = new long[2][2][k+1][n+1];
		for(int i=0;i<2;i++){
			for(int j=0;j<2;j++){
				for(int x=0;x<=k;x++){
					Arrays.fill(dp[i][j][x], -1);
				}
			}
		}
		long ans = (fun(0, 0, 1, 1) + fun(1, 1, 1, 1) + fun(0, 1, 1, 2) + fun(1, 0, 1, 2))%mod;
		out.println(ans);
		// N = n; K = k;
		// dp = new long[2][2][K+1][N+1];
		// for(long a[][][] : dp) {
		// 	for(long b[][] : a) {
		// 		for(long c[] : b) {
		// 			Arrays.fill(c, -1);
		// 		}
		// 	}
		// }
		// long res = (go(0,0,1,1)+go(0,1,2,1)+go(1,0,2,1)+go(1,1,1,1))%mod;
		// out.println(res);

	}
	static long go(int p1, int p2, int k, int ind) {
		if(k > K) return 0;
		if(ind >= N) return k == K ? 1 : 0;
		if(dp[p1][p2][k][ind] != -1) return dp[p1][p2][k][ind];
		long res = 0;
		if(p1==0&&p2==0) {
			res += go(0,0,k,ind+1);
			res += go(0,1,k+1,ind+1);
			res += go(1,0,k+1,ind+1);
			res += go(1,1,k+1,ind+1);
		}
		else if(p1==0&&p2==1) {
			res += go(0,1,k,ind+1);
			res += go(1,0,k+2,ind+1);
			res += go(0,0,k,ind+1);
			res += go(1,1,k,ind+1);
		}
		else if(p1==1&&p2==0) {
			res += go(1,0,k,ind+1);
			res += go(0,1,k+2,ind+1);
			res += go(0,0,k,ind+1);
			res += go(1,1,k,ind+1);
		}
		else {
			res += go(1,1,k,ind+1);
			res += go(0,1,k+1,ind+1);
			res += go(1,0,k+1,ind+1);
			res += go(0,0,k+1,ind+1);
		}
		return dp[p1][p2][k][ind] = res%mod;
	}
	static long fun(int prevDown, int prevUp, int i, int c){
		// System.out.println("i="+i+" c="+c);
		long ans = 0;
		if(c>k) return 0;
		if(i>=n){	
			if(c==k) return 1;
			return 0;
		} 
		if(dp[prevDown][prevUp][c][i]!=-1) return dp[prevDown][prevUp][c][i];
		if(prevDown==0 && prevUp==0){
			ans += fun(0, 0, i+1, c);
			ans += fun(1, 1, i+1, c+1);
			ans += fun(0, 1, i+1, c+1);
			ans += fun(1, 0, i+1, c+1);
		}
		else if(prevUp==0 && prevDown==1){
			ans += fun(0, 0, i+1, c);
			ans += fun(1, 1, i+1, c);
			ans += fun(0, 1, i+1, c);
			ans += fun(1, 0, i+1, c+2);
		}
		else if(prevUp==1 && prevDown==0){
			ans += fun(0, 0, i+1, c);
			ans += fun(1, 1, i+1, c);
			ans += fun(0, 1, i+1, c+2);
			ans += fun(1, 0, i+1, c);
		}
		else{
			ans += fun(0, 0, i+1, c+1);
			ans += fun(1, 1, i+1, c);
			ans += fun(0, 1, i+1, c+1);
			ans += fun(1, 0, i+1, c+1);
		}
		return dp[prevDown][prevUp][c][i] = ans%mod;
	}
	
	void run() throws Exception
	{
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new D().run(); }
	
	private byte[] inbuf = new byte[1024];
	public 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 static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}