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 CPP):

Solution:
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <cstring>
#define FOR(i,n) for(int i = 0; i < (n); i++)
#define sz(c) ((int)(c).size())
#define ten(x) ((int)1e##x)
#define MOD 998244353
#define SIZE 200005

using namespace std;
typedef long long int ll;
template<class T> T extgcd(T a, T b, T& x, T& y) { for (T u = y = 1, v = x = 0; a;) { T q = b / a; swap(x -= q * u, u); swap(y -= q * v, v); swap(b -= q * a, a); } return b; }
template<class T> T mod_inv(T a, T m) { T x, y; extgcd(a, m, x, y); return (m + x % m) % m; }
ll mod_pow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }

template<int mod, int primitive_root>
class NTT {
public:
	int get_mod() const { return mod; }
	void _ntt(vector<ll>& a, int sign) {
		const int n = sz(a);
		//assert((n ^ (n&-n)) == 0); //n = 2^k
		const int g = 3; //g is primitive root of mod
		int h = (int)mod_pow(g, (mod - 1) / n, mod); // h^n = 1
		if (sign == -1) h = (int)mod_inv(h, mod); //h = h^-1 % mod
		//bit reverse
		int i = 0;
		for (int j = 1; j < n - 1; ++j) {
			for (int k = n >> 1; k >(i ^= k); k >>= 1);
			if (j < i) swap(a[i], a[j]);
		}
		for (int m = 1; m < n; m *= 2) {
			const int m2 = 2 * m;
			const ll base = mod_pow(h, n / m2, mod);
			ll w = 1;
			FOR(x, m) {
				for (int s = x; s < n; s += m2) {
					ll u = a[s];
					ll d = a[s + m] * w % mod;
					a[s] = u + d;
					if (a[s] >= mod) a[s] -= mod;
					a[s + m] = u - d;
					if (a[s + m] < 0) a[s + m] += mod;
				}
				w = w * base % mod;
			}
		}
		for (int i=0;i<a.size();i++) if (a[i] < 0) a[i] += mod;
	}
	void ntt(vector<ll>& input) {
		_ntt(input, 1);
	}
	void intt(vector<ll>& input) {
		_ntt(input, -1);
		const int n_inv = mod_inv(sz(input), mod);
		for (int i=0;i<input.size();i++) input[i] = input[i] * n_inv % mod;
	}
	vector<ll> convolution(const vector<ll>& a, const vector<ll>& b){
		int ntt_size = 1;
		while (ntt_size < sz(a) + sz(b)) ntt_size *= 2;
		vector<ll> _a = a, _b = b;
		_a.resize(ntt_size); _b.resize(ntt_size);
		ntt(_a);
		ntt(_b);
		FOR(i, ntt_size){
			(_a[i] *= _b[i]) %= mod;
		}
		intt(_a);
		return _a;
	}
};
NTT <MOD,3> solve;
ll fac[SIZE],finv[SIZE],inv[SIZE];
ll dp[SIZE];

void make()
{
	inv[1]=1;
	fac[0]=fac[1]=1;
	finv[0]=finv[1]=1;
	for(int i=2;i<SIZE;i++)
	{
		inv[i]=MOD-inv[MOD%i]*(ll) (MOD/i)%MOD;
		fac[i]=fac[i-1]*(ll) i%MOD;
		finv[i]=finv[i-1]*inv[i]%MOD;
	}
}
ll C(int a,int b)
{
	if(a<b) return 0;
	return fac[a]*(finv[b]*finv[a-b]%MOD)%MOD;
}
int main()
{
	make();
	int n,m;
	scanf("%d %d",&n,&m);
	dp[0]=1;
	for(int i=0;i<m;i++)
	{
		//n -> n+k の時に、(n+k+2)! / (k+2)! / n! * dp[n] 
		vector <ll> A,B;
		for(int j=0;j<=n;j++) A.push_back(dp[j]*finv[j]%MOD);
		for(int k=0;k<=n;k++) B.push_back(finv[k+2]);
		vector <ll> gt=solve.convolution(A,B);
		for(int j=0;j<=n;j++) dp[j]=(gt[j]*fac[j+2]%MOD-dp[j]*(ll) j%MOD+MOD)%MOD;
		//for(int j=0;j<=n;j++) printf("%lld ",dp[j]);puts("");
	}
	ll ret=0;
	for(int i=0;i<=n;i++) ret=(ret+dp[i]*C(n,i)%MOD)%MOD;
	printf("%lld\n",ret);
	return 0;
}