Problem: PolandBall is standing in a row with Many Other Balls. More precisely, there are exactly n Balls. Balls are proud of their home land — and they want to prove that it's strong.

The Balls decided to start with selecting exactly m groups of Balls, each consisting either of single Ball or two neighboring Balls. Each Ball can join no more than one group.

The Balls really want to impress their Enemies. They kindly asked you to calculate number of such divisions for all m where 1 ≤ m ≤ k. Output all these values modulo 998244353, the Enemies will be impressed anyway.

Input

There are exactly two numbers n and k (1 ≤ n ≤ 109, 1 ≤ k < 215), denoting the number of Balls and the maximim number of groups, respectively.

Output

You should output a sequence of k values. The i-th of them should represent the sought number of divisions into exactly i groups, according to PolandBall's rules.

Examples

Input

3 3


Output

5 5 1 

Input

1 1


Output

1 

Input

5 10


Output

9 25 25 9 1 0 0 0 0 0 

Note

In the first sample case we can divide Balls into groups as follows: 

{1}, {2}, {3}, {12}, {23}.

{12}{3}, {1}{23}, {1}{2}, {1}{3}, {2}{3}.

{1}{2}{3}.

Therefore, output is: 5 5 1.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class G {

	int LOG = 16;
	int len = 1 << LOG;

	final int MOD = 7 * 17 * (1 << 23) + 1;
	int G = 3;

	int pow(int a, int b) {
		int res = 1;
		while (b > 0) {
			if ((b & 1) == 1) {
				res = (int) ((1L * res * a) % MOD);
			}
			a = (int) ((1L * a * a) % MOD);
			b >>= 1;
		}
		return res;
	}

	int[] tail = new int[len], omega = new int[len];

	void FFT(int[] a, boolean inv) {
		for (int i = 0; i < len; i++) {
			if (i < tail[i]) {
				int tmp = a[i];
				a[i] = a[tail[i]];
				a[tail[i]] = tmp;
			}
		}

		for (int len = 2; len <= a.length; len *= 2) {
			for (int i = 0; i < a.length; i += len) {
				int pos = 0;
				for (int j = 0, k = len / 2; k < len; j++, k++) {
					int u = a[i + j], v = (int) ((1L * a[i + k] * omega[pos]) % MOD);

					a[i + j] = u + v;
					if (a[i + j] >= MOD) {
						a[i + j] -= MOD;
					}
					a[i + k] = u - v;
					if (a[i + k] < 0) {
						a[i + k] += MOD;
					}

					if (inv) {
						pos -= a.length / len;
						if (pos < 0) {
							pos += a.length;
						}
					} else {
						pos += a.length / len;
					}
				}
			}
		}
		if (inv) {
			int coef = pow(a.length, MOD - 2);
			for (int i = 0; i < a.length; i++) {
				a[i] = (int) ((1L * a[i] * coef) % MOD);
			}
		}
	}

	void prepare() {
		int om = pow(G, (MOD - 1) / len);
		omega[0] = 1;
		for (int i = 1; i < len; i++) {
			omega[i] = (int) ((1L * omega[i - 1] * om) % MOD);
			tail[i] = ((tail[i >> 1] >> 1) | ((i & 1) << (LOG - 1)));
		}
	}

	int k;

	void trunc(int[] ans) {
		for (int j = k + 1; j < len; j++) {
			ans[j] = 0;
		}
	}

	Map<Integer, int[]> memo = new HashMap<>();
	Map<Integer, int[]> memoFT = new HashMap<>();
	
	int[][] dp;
	
	void fillStupid(int mx) {
		dp = new int[mx + 1][k + 1];
		dp[0][0] = 1;
		for (int i = 1; i <= mx; i++) {
			for (int j = 0; j <= i && j <= k; j++) {
				dp[i][j] = dp[i - 1][j];
				if (i - 1 >= 0 && j > 0) {
					dp[i][j] += dp[i - 1][j - 1];
					dp[i][j] %= MOD;
				}
				if (i - 2 >= 0 && j > 0) {
					dp[i][j] += dp[i - 2][j - 1];
					dp[i][j] %= MOD;
				}
			}
		}
		
		for (int i = 0; i <= mx; i++) {
			dp[i] = Arrays.copyOf(dp[i], len);
		}
	}
	
	int[] stupid(int n) {
		return dp[n];
	}
	
	int[] res = new int[len];

	int[] get(int n) {
		if (memo.containsKey(n)) {
			return memo.get(n);
		}

		int[] result = new int[len];
		if (n <= 8) {
			result = stupid(n);
		} else {
			int size1 = (n + 1) / 2, size2 = n / 2;
			for (int midLeft = 0; midLeft <= 0; midLeft++) {
				for (int midRight = 0; midRight + midLeft <= 0; midRight++) {
					get(size1 - midLeft);
					get(size2 - midRight);

					int[] tmp1 = memoFT.get(size1 - midLeft), tmp2 = memoFT.get(size2 - midRight);
					multiply(res, tmp1, tmp2);

					int add = Math.min(1, midLeft + midRight);
					for (int i = 0; i + add < len; i++) {
						if (i + add < len) {
							result[i + add] += res[i];
							if (result[i + add] >= MOD) {
								result[i + add] -= MOD;
							}
						}
					}
				}
			}
			
			
			for (int midLeft = 1; midLeft <= 1; midLeft++) {
				for (int midRight = 1; midRight + midLeft <= 2; midRight++) {
					get(size1 - midLeft);
					get(size2 - midRight);

					int[] tmp1 = memoFT.get(size1 - midLeft), tmp2 = memoFT.get(size2 - midRight);
					multiply(res, tmp1, tmp2);

					int add = Math.min(1, midLeft + midRight);
					for (int i = 0; i + add < len; i++) {
						if (i + add < len) {
							result[i + add] += res[i];
							if (result[i + add] >= MOD) {
								result[i + add] -= MOD;
							}
						}
					}
				}
			}
		}
		trunc(result);
		memo.put(n, result);
		int[] resultFT = result.clone();
		FFT(resultFT, false);
		memoFT.put(n, resultFT);
		return result;
	}

	void multiply(int[] res, int[] a, int[] b) {
		for (int i = 0; i < len; i++) {
			res[i] = (int) (1L * a[i] * b[i] % MOD);
		}
		FFT(res, true);
	}

	void solve() {
		prepare();
		int n = in.nextInt();
		k = in.nextInt();
		fillStupid(8);
		fast(n, k);
	}

	void print(int[] a) {
		System.err.println(Arrays.toString(Arrays.copyOf(a, 100)));
	}

	void fast(int n, int k) {
		memo = new HashMap<>();
		memoFT = new HashMap<>();
		for (int i = 1; i <= k; i++) {
			long result = 0;
			result += get(n)[i];
			out.print((result % MOD) + " ");
		}
		out.println();
	}

	FastScanner in;
	PrintWriter out;

	void run() {
		in = new FastScanner();
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}

		public String nextToken() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
				}
			}
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextToken());
		}

		public long nextLong() {
			return Long.parseLong(nextToken());
		}

		public double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}

	public static void main(String[] args) {
		new G().run();
	}
}