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.BufferedInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.util.Arrays;

public class E2 {

	static int N;
	static int K;
	static int mod = 998244353;
	static long modInvOf2;
	static int dp[][][][];
	static int up[][][][];
	static int pow2[];
	static int iter = -1;
	public static void main(String[] args) {
		JS in = new JS();
		N = in.nextInt();
		K = in.nextInt();
		modInvOf2 = modInv(2, mod);
		dp = new int[2][2][N+1][N+1];
		up = new int[2][2][N+1][N+1];
		long regular[] = new long[N+1];
		pow2 = new int[600];
		pow2[0] = 1;
		for(int i = 1; i < 600; i++) {
			pow2[i] = pow2[i-1]*2;
			if(pow2[i] >= mod) pow2[i] -= mod;
		}
	
		for(int run = 1; run <= N; run++) {
			iter = run;
			regular[run] = go(1, run==1?1:0, 1, 1, run) + go(0, run==1?1:0, 1, 1, run);
			if(regular[run] >= mod) regular[run] -= mod;
		}
		long other[] = new long[N+1];
		for(int i = 1; i <= N; i++) {
			for(int j = 1; j <= i; j++) {
				other[i] += regular[j];
				if(other[i] >= mod) other[i] -= mod;
			}
		}
		
		
		long res = 0;
		for(int run = 1; run <= N; run++) {
			long max = K/run;
			if(K%run == 0) max--;
			if(max == 0) continue;
			res += (regular[run]*other[Math.min(N,(int)max)])%mod;
			if(res >= mod) res -= mod;
		}
		res = ((res*modInvOf2)%mod+mod)%mod;
		System.out.println(res);
		
	}
	static int go(int bit, int have, int index, int cur, int goal) {
		if(index >= N) return have;
		if(cur + (N-index) < goal) return have*pow2[N-index];
		if(up[bit][have][index][cur] == iter) return dp[bit][have][index][cur];
//		//take
		int take = -1;
		if(bit == 0) {
			take = go(1, have, index+1, 1, goal);
		}
		else {
			if(cur+1 > goal) take = 0;
			else take = go(1, have | (cur+1 == goal ? 1 : 0), index+1, cur+1, goal);
		}
		//leave
		int leave = -1;
		if(bit == 1) {
			leave = go(0, have, index+1, 1, goal);
		}
		else {
			if(cur+1 > goal) leave = 0;
			else leave = go(0, have | (cur+1 == goal? 1 : 0), index+1, cur+1, goal);
		}
		int res = take+leave;
		if(res >= mod) res -= mod;
		up[bit][have][index][cur] = iter;
		return dp[bit][have][index][cur] = res;
	}

	static long modInv(long x, long mod) {
		if(x == 1) return 1;
		long r = mod % x;
		return modInv(r, x % r, 0, 1, mod / x, x / r);
	}
	static long modInv(long a, long b, long y0, long y1, long q0, long q1) {
		long y2 = y0 - y1*q0;
		return b == 0 ? y2 : modInv(b, a % b, y1, y2, q1, a / b);
	}
	
	static class JS{
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;
		
		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}
		
		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}
		
		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}				
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}
		
		public int nextInt() {
			return (int)nextLong();
		}
		
		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}
		
		public double nextDouble() {
		    while(c!='.'&&c!='-'&&(c <'0' || c>'9')) c = nextChar();
		    boolean neg = c=='-';
		    if(neg)c=nextChar();
		    boolean fl = c=='.';
		    double cur = nextLong();
		    if(fl) return neg ? -cur/num : cur/num;
		    if(c == '.') {
			double next = nextLong();
			return neg ? -cur-next/num : cur+next/num;
		    }
		    else return neg ? -cur : cur;
		}
		
		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}
		
		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
	}
	
}
