You are given a square board, consisting of n rows and n columns. Each tile in it should be colored either white or black.

Let's call some coloring beautiful if each pair of adjacent rows are either the same or different in every position. The same condition should be held for the columns as well.

Let's call some coloring suitable if it is beautiful and there is no rectangle of the single color, consisting of at least k tiles.

Your task is to count the number of suitable colorings of the board of the given size.

Since the answer can be very large, print it modulo 998244353.

Input

A single line contains two integers n and k (1 ≤ n ≤ 500, 1 ≤ k ≤ n^2) — the number of rows and columns of the board and the maximum number of tiles inside the rectangle of the single color, respectively.

Output

Print a single integer — the number of suitable colorings of the board of the given size modulo 998244353.

Examples

Input

1 1


Output

0


Input

2 3


Output

6


Input

49 1808


Output

359087121

Note

Board of size 1 × 1 is either a single black tile or a single white tile. Both of them include a rectangle of a single color, consisting of 1 tile.

Here are the beautiful colorings of a board of size 2 × 2 that don't include rectangles of a single color, consisting of at least 3 tiles:

<image>

The rest of beautiful colorings of a board of size 2 × 2 are the following:

<image>
import java.io.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.List;
 import java.util.*;
 public class realfast implements Runnable 
  {
    private static final int INF = (int) 1e9;
    long in= (long)Math.pow(10,9)+7;
    long fac[]= new long[3000];
    public  void solve() throws IOException 
    {
        long m =  998244353;
        int n  = readInt();
        int k = readInt();
        long sum[]= new long[n+1];
        sum[0]=0;
        for(int i=1;i<=n;i++)
        {
            long dp[]= new long[n+2];
            dp[n+1]=1;
            for(int j=n;j>=1;j--)
            {
                for(int l=1;l<=Math.min(i,n-j+1);l++)
                {
                    dp[j]= (dp[j]%m+ dp[j+l]%m)%m;
                }
            }
            sum[i]= (dp[1])%m;
        }
        long val =0;
        
        //out.println();
        for(int i=1;i<=n;i++)
        {

            int j = k/i;
            if(k%i==0)
                j--;
            j=Math.min(n,j);
            val = (val%m + (((sum[i]%m-sum[i-1]%m+m)%m)*(sum[j]%m))%m)%m;
        }
        val = (val*2)%m;
        out.println(val);

    }
    public int seg(int seg[], int left, int right, int index, int val)
    {
        if(left==right)
        {
            seg[index]=1;
            return 1;
        }
        int mid = left+(right-left)/2;

        if(val<=mid)
        {
            seg(seg,left,mid,2*index+1,val);
        }
        else
        {
            seg(seg,mid+1,right,2*index+2,val);
        }
        seg[index]= seg[2*index+1]+seg[2*index+2];
        return seg[index];
    }
    public int val(int seg[], int left , int right, int l , int r,int index)
    {
            if(left>r||right<l)
            {
               return 0;
            }
            int mid = left+(right-left)/2;
            if(left>=l&&right<=r)
            return seg[index];

            return val(seg,left,mid,l,r,2*index+1)+val(seg,mid+1,right,l,r,2*index+2);
    }
    public int gcd(int a , int b )
    {
      if(a<b)
      {
        int t =a;
        a=b;
        b=t;
      }
      if(a%b==0)
        return b ;
      return gcd(b,a%b);
    }
    public long pow(long n , long p,long m)
    {
         if(p==0)
            return 1;
        long val = pow(n,p/2,m);;
        val= (val*val)%m;
        if(p%2==0)
            return val;
        else
            return (val*n)%m;
    }
    
    
    ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) {
        new Thread(null, new realfast(), "", 128 * (1L << 20)).start();
    }
 
    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private PrintWriter out;
 
    @Override
    public void run() {
        try {
            if (ONLINE_JUDGE || !new File("input.txt").exists()) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                reader = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }
            solve();
        } catch (IOException e) {
            throw new RuntimeException(e);
        } finally {
            try {
                reader.close();
            } catch (IOException e) {
                // nothing
            }
            out.close();
        }
    }
 
    private String readString() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
 
    @SuppressWarnings("unused")
    private int readInt() throws IOException {
        return Integer.parseInt(readString());
    }
 
    @SuppressWarnings("unused")
    private long readLong() throws IOException {
        return Long.parseLong(readString());
    }
 
    @SuppressWarnings("unused")
    private double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }
}
class edge implements Comparable<edge>{
    int val ;
    int color;
    
    edge(int u, int v)
    {
       this.val=u;
       this.color=v;
    }
    public int compareTo(edge e)
    {
        return this.val-e.val;
    }
}