Problem: We have an N \times M grid. The square at the i-th row and j-th column will be denoted as (i,j). Particularly, the top-left square will be denoted as (1,1), and the bottom-right square will be denoted as (N,M). Takahashi painted some of the squares (possibly zero) black, and painted the other squares white.

We will define an integer sequence A of length N, and two integer sequences B and C of length M each, as follows:

* A_i(1\leq i\leq N) is the minimum j such that (i,j) is painted black, or M+1 if it does not exist.
* B_i(1\leq i\leq M) is the minimum k such that (k,i) is painted black, or N+1 if it does not exist.
* C_i(1\leq i\leq M) is the maximum k such that (k,i) is painted black, or 0 if it does not exist.



How many triples (A,B,C) can occur? Find the count modulo 998244353.

Constraints

* 1 \leq N \leq 8000
* 1 \leq M \leq 200
* N and M are integers.



Partial Score

* 1500 points will be awarded for passing the test set satisfying N\leq 300.

Constraints

* 1 \leq N \leq 8000
* 1 \leq M \leq 200
* N and M are integers.

Input

Input is given from Standard Input in the following format:


N M

Output

Print the number of triples (A,B,C), modulo 998244353.

Examples

Input

2 3


Output

64


Input

4 3


Output

2588


Input

17 13


Output

229876268


Input

5000 100


Output

57613837

Solution (in JAVA):

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

public class Main {

	ModuloCombinatorics mc = new ModuloCombinatorics(10000, P);

	static final int P = 998244353;

	static int nextPowerOf2(int x) {
		return x == 1 ? 1 : Integer.highestOneBit(x - 1) << 1;
	}

	static class CompV {
		double[] re, im;

		void add(CompV o) {
			for (int i = 0; i < re.length; i++) {
				re[i] += o.re[i];
				im[i] += o.im[i];
			}
		}

		static CompV times(CompV a, CompV b) {
			double[] aRe = a.re;
			double[] aIm = a.im;
			double[] bRe = b.re;
			double[] bIm = b.im;
			double[] re = new double[aRe.length];
			double[] im = new double[aRe.length];

			for (int i = 0; i < aRe.length; i++) {
				re[i] = aRe[i] * bRe[i] - aIm[i] * bIm[i];
				im[i] = aRe[i] * bIm[i] + aIm[i] * bRe[i];
			}

			return new CompV(re, im);
		}

		static CompV plus(CompV a, CompV b) {
			double[] aRe = a.re;
			double[] aIm = a.im;
			double[] bRe = b.re;
			double[] bIm = b.im;
			double[] re = new double[aRe.length];
			double[] im = new double[aRe.length];

			for (int i = 0; i < aRe.length; i++) {
				re[i] = aRe[i] + bRe[i];
				im[i] = aIm[i] + bIm[i];
			}

			return new CompV(re, im);
		}

		/**
		 * @return a + bi
		 */
		static CompV packFFT(CompV a, CompV b) {
			double[] aRe = a.re;
			double[] aIm = a.im;
			double[] bRe = b.re;
			double[] bIm = b.im;
			double[] re = new double[aRe.length];
			double[] im = new double[aRe.length];
			for (int i = 0; i < aRe.length; i++) {
				re[i] = aRe[i] - bIm[i];
				im[i] = aIm[i] + bRe[i];
			}
			return new CompV(re, im);
		}

		/**
		 * for real-valued a and b restores FFT(a) and FFT(b) from FFT(a + bi)
		 */
		void unpackFFT(CompV a, CompV b) {
			int n = re.length;
			double[] aRe = a.re;
			double[] aIm = a.im;
			double[] bRe = b.re;
			double[] bIm = b.im;
			for (int i = 0; i < n; i++) {
				int j = i == 0 ? 0 : n - i;
				aRe[i] = (re[i] + re[j]) * 0.5;
				aIm[i] = (im[i] - im[j]) * 0.5;
				bRe[i] = (im[i] + im[j]) * 0.5;
				bIm[i] = (re[j] - re[i]) * 0.5;
			}
		}

		public CompV(double[] re, double[] im) {
			this.re = re;
			this.im = im;
		}

		public CompV(int len) {
			re = new double[len];
			im = new double[len];
		}
	}

	static final int L = (int) Math.sqrt(P);
	static final int L2 = L * L;

	public static int[] multFaster(int[] a, int[] b) {
		int len = nextPowerOf2(a.length + b.length - 1);

		double[] p1 = new double[len];
		double[] q1 = new double[len];
		for (int i = 0; i < a.length; i++) {
			p1[i] = a[i] % L;
			q1[i] = a[i] / L;
		}

		double[] p2 = new double[len];
		double[] q2 = new double[len];
		for (int i = 0; i < b.length; i++) {
			p2[i] = b[i] % L;
			q2[i] = b[i] / L;
		}

		CompV p1p2Pack = new CompV(p1, p2);
		CompV q1q2Pack = new CompV(q1, q2);

		fft(p1p2Pack, false);
		fft(q1q2Pack, false);

		CompV fp1 = new CompV(len);
		CompV fp2 = new CompV(len);
		p1p2Pack.unpackFFT(fp1, fp2);

		CompV fq1 = new CompV(len);
		CompV fq2 = new CompV(len);
		q1q2Pack.unpackFFT(fq1, fq2);

		CompV back0 = CompV.times(fp1, fp2);

		CompV back1 = CompV.times(fp1, fq2);
		back1.add(CompV.times(fq1, fp2));

		CompV back2 = CompV.times(fq1, fq2);

		CompV back01 = CompV.packFFT(back0, back1);

		fft(back01, true);
		fft(back2, true);

		int[] ret = new int[len];

		for (int i = 0; i < len; i++) {
			long v0 = Math.round(back01.re[i]) % P;
			long v1 = Math.round(back01.im[i]) % P * L % P;
			long v2 = Math.round(back2.re[i]) % P * L2 % P;
			ret[i] = (int) ((v0 + v1 + v2) % P);
		}

		return ret;
	}

	public static void fft(CompV v, boolean invert) {
		double[] a = v.re;
		double[] b = v.im;
		int n = a.length;
		int shift = 32 - Integer.numberOfTrailingZeros(n);
		prepareArrays(32 - shift);
		int[] rev = rev2D[32 - shift];
		// System.err.println(n + " " + shift);
		for (int i = 1; i < n; i++) {
			int j = rev[i];
			if (i < j) {
				double temp = a[i];
				a[i] = a[j];
				a[j] = temp;
				temp = b[i];
				b[i] = b[j];
				b[j] = temp;
			}
		}

		// this shit looks awkward
		double multInv = invert ? -1 : 1;

		for (int len = 2, row = 0; len <= n; len <<= 1, row++) {
			int halfLen = len >> 1;
			double[] multReArr = powRe[row];
			double[] multImArr = powIm[row];
			for (int i = 0; i < n; i += len) {
				int toJ = i + halfLen;

				for (int j1 = i, j2 = toJ, k = 0; k < halfLen; j1++, j2++, k++) {
					double uA = a[j1];
					double uB = b[j1];

					double multRe = multReArr[k];
					double multIm = multImArr[k] * multInv;

					double vA = a[j2] * multRe - b[j2] * multIm;
					double vB = a[j2] * multIm + b[j2] * multRe;
					a[j1] = uA + vA;
					b[j1] = uB + vB;
					a[j2] = uA - vA;
					b[j2] = uB - vB;
				}
			}
		}
		if (invert) {
			for (int i = 0; i < n; i++) {
				a[i] /= n;
				b[i] /= n;
			}
		}
	}

	static double[][] powRe = { { 1 } };
	static double[][] powIm = { { 0 } };
	static int[][] rev2D = {};

	static void prepareArrays(int n) {

		if (rev2D.length < n + 1) {
			rev2D = Arrays.copyOf(rev2D, n + 1);
		}

		if (rev2D[n] == null) {
			int[] tmp = rev2D[n] = new int[1 << n];
			for (int i = 0; i < (1 << n); i++) {
				tmp[i] = tmp[i >> 1] >> 1;
				if ((i & 1) == 1) {
					tmp[i] |= 1 << (n - 1);
				}
			}
		}

		int oldN = powRe.length;

		if (oldN >= n) {
			return;
		}

		powRe = Arrays.copyOf(powRe, n);
		powIm = Arrays.copyOf(powIm, n);

		for (int i = oldN; i < n; i++) {

			double angle = Math.PI / (1 << i);

			double multRe = Math.cos(angle);
			double multIm = Math.sin(angle);

			double[] toRe = powRe[i] = new double[1 << i];
			double[] toIm = powIm[i] = new double[1 << i];

			double[] fromRe = powRe[i - 1];
			double[] fromIm = powIm[i - 1];

			for (int j = 0; j < 1 << (i - 1); j++) {

				double re = fromRe[j];
				double im = fromIm[j];

				toRe[j << 1] = re;
				toIm[j << 1] = im;
				toRe[(j << 1) | 1] = re * multRe - im * multIm;
				toIm[(j << 1) | 1] = re * multIm + im * multRe;
			}

			// System.err.println(Arrays.toString(toRe));
			// System.err.println(Arrays.toString(toIm));
		}
	}

	void submit() {
		int r = nextInt();
		int c = nextInt();
		int[] dp = new int[r + 1];
		Arrays.fill(dp, 1);
		c--;

		int[] invFact = mc.invFact;
		int[] fact = mc.fact;
		
		int[] two = new int[r + 1];
		for (int i = 1; i <= r; i++) {
			two[i] = invFact[i + 2];
		}

		while (c-- > 0) {
			int[] tmp = new int[r + 1];
			for (int i = 0; i <= r; i++) {
				tmp[i] = (int)((long)dp[i] * invFact[i] % P);
			}
			int[] next = multFaster(tmp, two);
			next = Arrays.copyOf(next, r + 1);
			for (int i = 0; i <= r; i++) {
				next[i] = (int)((long)next[i] * fact[i + 2] % P);
			}
			for (int i = 0; i <= r; i++) {
				int ways = 1 + (i + 1) * i / 2;
				next[i] += (int) ((long) dp[i] * ways % P);
				if (next[i] >= P) {
					next[i] -= P;
				}
			}
			dp = next;
		}

		int ret = 0;
		for (int i = 0; i <= r; i++) {
			ret += (int) ((long) mc.choose(r, i) * dp[i] % P);
			if (ret >= P) {
				ret -= P;
			}
		}
		
		out.println(ret);
	}

	static class ModuloCombinatorics {
		/** maximal needed number, N itself is included **/
		final int N;

		/** prime modulo **/
		final int P;

		/** factorials **/
		final int[] fact;

		/** multiplicative inverses, take care to not touch inv[0] **/
		final int[] inv;

		/** inverse factorials **/
		final int[] invFact;

		public ModuloCombinatorics(int N, int P) {
			this.N = N;
			this.P = P;
			fact = new int[N + 1];
			fact[0] = 1;
			for (int i = 1; i <= N; i++) {
				fact[i] = (int) ((long) i * fact[i - 1] % P);
			}

			inv = new int[N + 1];
			inv[1] = 1;
			for (int i = 2; i <= N; i++) {
				inv[i] = P - (int) ((long) (P / i) * inv[P % i] % P);
			}

			invFact = new int[N + 1];
			invFact[0] = 1;
			for (int i = 1; i <= N; i++) {
				invFact[i] = (int) ((long) invFact[i - 1] * inv[i] % P);
			}
		}

		public int choose(int n, int k) {
			return (n < 0 || k < 0 || k > n) ? 0 : (int) ((long) fact[n]
					* invFact[k] % P * invFact[n - k] % P);
		}

		/** a^b modulo mod, mod is arbitrary **/
		static public int pow(int a, long b, int mod) {
			if (a < 0 || a >= mod || b < 0) {
				throw new IllegalArgumentException();
			}
			int ret = 1;
			for (; b > 0; b >>= 1) {
				if ((b & 1) == 1) {
					ret = (int) ((long) ret * a % mod);
				}
				a = (int) ((long) a * a % mod);
			}
			return ret;
		}

		/** a^b modulo P **/
		public int pow(int a, long b) {	
			return pow(a, b, P);
		}
	}

	void preCalc() {

	}

	void test() {

	}

	void stress() {
		for (int tst = 0;; tst++) {
			if (false) {
				throw new AssertionError();
			}
			System.err.println(tst);
		}
	}

	Main() throws IOException {
		is = System.in;
		out = new PrintWriter(System.out);
		preCalc();
		submit();
		// stress();
		// test();
		out.close();
	}

	static final Random rng = new Random();
	static final int C = 5;

	static int rand(int l, int r) {
		return l + rng.nextInt(r - l + 1);
	}

	public static void main(String[] args) throws IOException {
		new Main();
	}

	private InputStream is;
	PrintWriter out;

	private byte[] buf = new byte[1 << 14];
	private int bufSz = 0, bufPtr = 0;

	private int readByte() {
		if (bufSz == -1)
			throw new RuntimeException("Reading past EOF");
		if (bufPtr >= bufSz) {
			bufPtr = 0;
			try {
				bufSz = is.read(buf);
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
			if (bufSz <= 0)
				return -1;
		}
		return buf[bufPtr++];
	}

	private boolean isTrash(int c) {
		return c < 33 || c > 126;
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isTrash(b))
			;
		return b;
	}

	String nextToken() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!isTrash(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	String nextString() {
		int b = readByte();
		StringBuilder sb = new StringBuilder();
		while (!isTrash(b) || b == ' ') {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

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

	char nextChar() {
		return (char) skip();
	}

	int nextInt() {
		int ret = 0;
		int b = skip();
		if (b != '-' && (b < '0' || b > '9')) {
			throw new InputMismatchException();
		}
		boolean neg = false;
		if (b == '-') {
			neg = true;
			b = readByte();
		}
		while (true) {
			if (b >= '0' && b <= '9') {
				ret = ret * 10 + (b - '0');
			} else {
				if (b != -1 && !isTrash(b)) {
					throw new InputMismatchException();
				}
				return neg ? -ret : ret;
			}
			b = readByte();
		}
	}

	long nextLong() {
		long ret = 0;
		int b = skip();
		if (b != '-' && (b < '0' || b > '9')) {
			throw new InputMismatchException();
		}
		boolean neg = false;
		if (b == '-') {
			neg = true;
			b = readByte();
		}
		while (true) {
			if (b >= '0' && b <= '9') {
				ret = ret * 10 + (b - '0');
			} else {
				if (b != -1 && !isTrash(b)) {
					throw new InputMismatchException();
				}
				return neg ? -ret : ret;
			}
			b = readByte();
		}
	}
}