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:
//package eightvc.e;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Map;

public class G2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	static int mod = 998244353;
	
	void solve()
	{
		int n = ni();
		int K = ni();
		long[][][] M = new long[][][]{
			{{1L, 1L}, {0L, 1L}},
			{{1L}, {}}
		};
		long[][] v = {
				{1L, 1L},
				{1L}
		};
		long[][] res = pow(M, v, n-1, K+1);
		for(int i = 1;i <= K;i++){
			out.print((i >= res[0].length ? 0 : res[0][i]) + " ");
		}
	}
	
	// A^e*v
	public static long[][] pow(long[][][] A, long[][] v, long e, int K)
	{
		long[][][] MUL = A;
		for(;e > 0;e>>>=1) {
			if((e&1)==1)v = mul(MUL, v, K);
			MUL = p2(MUL, K);
		}
		return v;
	}
	
	
	// int matrix * int vector
	public static long[][] mul(long[][][] A, long[][] v, int K)
	{
		int m = A.length;
		int n = v.length;
		long[][] w = new long[m][];
//		long[][][] cache = new long[2][2][];
		for(int i = 0;i < m;i++){
			long[] sum = new long[0];
			for(int k = 0;k < n;k++){
				sum = add(sum, mul(A[i][k], v[k], K));
			}
			w[i] = sum;
		}
		return w;
	}
	// caching
	
	// int matrix^2 (cannot ensure negative values)
	public static long[][][] p2(long[][][] A, int K)
	{
		int n = A.length;
		long[][][] C = new long[n][n][];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				long[] sum = new long[0];
				for(int k = 0;k < n;k++){
					sum = add(sum, mul(A[i][k], A[k][j], K));
				}
				C[i][j] = sum;
			}
		}
		return C;
	}
	
	public static int G = 3;
	
	public static long[] mul(long[] a, long[] b)
	{
		return Arrays.copyOf(convoluteSimply(a, b, mod, G), a.length+b.length-1);
	}
	
	public static long[] mul(long[] a, long[] b, int lim)
	{
		long[] res = convoluteSimply(a, b, mod, G);
		for(int i = Math.min(res.length-1, lim-1);i >= 0;i--){
			if(res[i] != 0){
				return Arrays.copyOf(res, i+1);
			}
		}
		return new long[0];
//		if(Math.max(a.length, b.length) >= 2000){
//			long[] res = convoluteSimply(a, b, mod, G);
//			for(int i = Math.min(res.length-1, lim-1);i >= 0;i--){
//				if(res[i] != 0){
//					return Arrays.copyOf(res, i+1);
//				}
//			}
//			return new long[0];
//		}else{
//			long[] res = mulnaive(a, b, lim);
//			for(int i = Math.min(res.length-1, lim-1);i >= 0;i--){
//				if(res[i] != 0){
//					return Arrays.copyOf(res, i+1);
//				}
//			}
//			return new long[0];
//		}
	}
	
	public static long[] mulnaive(long[] a, long[] b, int lim)
	{
		long[] c = new long[lim];
		long big = 8L*mod*mod;
		for(int i = 0;i < a.length;i++){
			for(int j = 0;j < b.length && i+j < lim;j++){
				c[i+j] += a[i]*b[j];
				if(c[i+j] >= big)c[i+j] -= big;
			}
		}
		for(int i = 0;i < c.length;i++)c[i] %= mod;
		return c;
	}

	public static long[] add(long[] a, long[] b)
	{
		long[] c = new long[Math.max(a.length, b.length)];
		for(int i = 0;i < a.length;i++)c[i] += a[i];
		for(int i = 0;i < b.length;i++)c[i] += b[i];
		for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod;
		return c;
	}
	
	public static long[] add(long[] a, long[] b, int lim)
	{
		long[] c = new long[lim];
		for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i];
		for(int i = 0;i < b.length && i < lim;i++)c[i] += b[i];
		for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod;
		for(int i = Math.min(c.length-1, lim-1);i >= 0;i--){
			if(c[i] != 0){
				return Arrays.copyOf(c, i+1);
			}
		}
		return new long[0];
	}

	
	public static final int[] NTTPrimes = {1053818881, 1051721729, 1045430273, 1012924417, 1007681537, 1004535809, 998244353, 985661441, 976224257, 975175681};
	public static final int[] NTTPrimitiveRoots = {7, 6, 3, 5, 3, 3, 3, 3, 3, 17};
//	public static final int[] NTTPrimes = {1012924417, 1004535809, 998244353, 985661441, 975175681, 962592769, 950009857, 943718401, 935329793, 924844033};
//	public static final int[] NTTPrimitiveRoots = {5, 3, 3, 3, 17, 7, 7, 7, 3, 5};
	
	static long h(long[] a)
	{
		long h = 1;
		for(long v : a){
			h = h * 1000000009 + v;
		}
		return h;
	}
	
	static long h(long[] a, int m)
	{
		return h(a)*1000000009 + m;
	}
	
	static Map<Long, long[]> cache = new HashMap<>();
	
	public static long[] convoluteSimply(long[] a, long[] b, int P, int g)
	{
		int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
		long[] fa = cache.computeIfAbsent(h(a, m), (z) -> nttmb(a, m, false, P, g));
		long[] fb = cache.computeIfAbsent(h(b, m), (z) -> nttmb(b, m, false, P, g));
		long[] ret = new long[m];
		for(int i = 0;i < m;i++){
			ret[i] = fa[i]*fb[i]%P;
		}
		return nttmb(ret, m, true, P, g);
	}
	
	public static long[] convoluteSimply(long[] a, long[] b, int P, int g, long[][][] cache, int ar, int ac, int br, int bc)
	{
		int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
		if(cache[ar][ac] == null){
			cache[ar][ac] = nttmb(a, m, false, P, g);;
		}
		if(cache[br][bc] == null){
			cache[br][bc] = nttmb(b, m, false, P, g);;
		}
		long[] fa = Arrays.copyOf(cache[ar][ac], cache[ar][ac].length);
		long[] fb = a == b ? fa : Arrays.copyOf(cache[br][bc], cache[br][bc].length);
		for(int i = 0;i < m;i++){
			fa[i] = fa[i]*fb[i]%P;
		}
		return nttmb(fa, m, true, P, g);
	}
	// static int[] wws = new int[270000]; // outer faster
	
	// Modifed Montgomery + Barrett
	private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g)
	{
		long[] dst = Arrays.copyOf(src, n);
		
		int h = Integer.numberOfTrailingZeros(n);
		long K = Integer.highestOneBit(P)<<1;
		int H = Long.numberOfTrailingZeros(K)*2;
		long M = K*K/P;
		
		int[] wws = new int[1<<h-1];
		long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P);
		long w = (1L<<32)%P;
		for(int k = 0;k < 1<<h-1;k++){
			wws[k] = (int)w;
			w = modh(w*dw, M, H, P);
		}
		long J = invl(P, 1L<<32);
		for(int i = 0;i < h;i++){
			for(int j = 0;j < 1<<i;j++){
				for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){
					long u = (dst[s] - dst[t] + 2*P)*wws[k];
					dst[s] += dst[t];
					if(dst[s] >= 2*P)dst[s] -= 2*P;
//					long Q = (u&(1L<<32)-1)*J&(1L<<32)-1;
					long Q = (u<<32)*J>>>32;
					dst[t] = (u>>>32)-(Q*P>>>32)+P;
				}
			}
			if(i < h-1){
				for(int k = 0;k < 1<<h-i-2;k++)wws[k] = wws[k*2];
			}
		}
		for(int i = 0;i < n;i++){
			if(dst[i] >= P)dst[i] -= P;
		}
		for(int i = 0;i < n;i++){
			int rev = Integer.reverse(i)>>>-h;
			if(i < rev){
				long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d;
			}
		}
		
		if(inverse){
			long in = invl(n, P);
			for(int i = 0;i < n;i++)dst[i] = modh(dst[i]*in, M, H, P);
		}
		
		return dst;
	}
	
	// Modified Shoup + Barrett
	private static long[] nttsb(long[] src, int n, boolean inverse, int P, int g)
	{
		long[] dst = Arrays.copyOf(src, n);
		
		int h = Integer.numberOfTrailingZeros(n);
		long K = Integer.highestOneBit(P)<<1;
		int H = Long.numberOfTrailingZeros(K)*2;
		long M = K*K/P;
		
		long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P);
		long[] wws = new long[1<<h-1];
		long[] ws = new long[1<<h-1];
		long w = 1;
		for(int k = 0;k < 1<<h-1;k++){
			wws[k] = (w<<32)/P;
			ws[k] = w;
			w = modh(w*dw, M, H, P);
		}
		for(int i = 0;i < h;i++){
			for(int j = 0;j < 1<<i;j++){
				for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){
					long ndsts = dst[s] + dst[t];
					if(ndsts >= 2*P)ndsts -= 2*P;
					long T = dst[s] - dst[t] + 2*P;
					long Q = wws[k]*T>>>32;
					dst[s] = ndsts;
					dst[t] = ws[k]*T-Q*P&(1L<<32)-1;
				}
			}
//			dw = dw * dw % P;
			if(i < h-1){
				for(int k = 0;k < 1<<h-i-2;k++){
					wws[k] = wws[k*2];
					ws[k] = ws[k*2];
				}
			}
		}
		for(int i = 0;i < n;i++){
			if(dst[i] >= P)dst[i] -= P;
		}
		for(int i = 0;i < n;i++){
			int rev = Integer.reverse(i)>>>-h;
			if(i < rev){
				long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d;
			}
		}
		
		if(inverse){
			long in = invl(n, P);
			for(int i = 0;i < n;i++){
				dst[i] = modh(dst[i] * in, M, H, P);
			}
		}
		
		return dst;
	}
	
	static final long mask = (1L<<31)-1;
	
	public static long modh(long a, long M, int h, int mod)
	{
		long r = a-((M*(a&mask)>>>31)+M*(a>>>31)>>>h-31)*mod;
		return r < mod ? r : r-mod;
	}
	
	private static long pow(long a, long n, long mod) {
		//		a %= mod;
		long ret = 1;
		int x = 63 - Long.numberOfLeadingZeros(n);
		for (; x >= 0; x--) {
			ret = ret * ret % mod;
			if (n << 63 - x < 0)
				ret = ret * a % mod;
		}
		return ret;
	}
	
	private static long invl(long a, long mod) {
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		return p < 0 ? p + mod : p;
	}

	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new G2().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 boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}