#include<bits/stdc++.h>
using namespace std;

#include<atcoder/all>
using namespace atcoder;
using mint=atcoder::modint998244353;

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

#define int long long

#define rep(i,n) for(int i=0;i<(n);i++)
#define rng(i,l,r) for(int i=(l);i<(r);i++)
#define rrep(i,n) for(int i=(n)-1;i>=0;i--)
#define rrng(i,l,r) for(int i=(r)-1;i>=(l);i--)

#define fi first
#define se second
#define all(x) (x).begin(),(x).end()

struct fast_io{fast_io(){std::cin.tie(nullptr)->sync_with_stdio(false);}}_;

template<long long mod,long long MAX_N>
struct factional_prime{
	long long inv_[MAX_N+1];
    long long fac_[MAX_N+1];
    long long fac_inv_[MAX_N+1];

    factional_prime(){
        inv_[0]=0;inv_[1]=fac_[0]=fac_[1]=fac_inv_[0]=fac_inv_[1]=1;
        for(long long i=2;i<=MAX_N;i++){
            inv_[i]=((mod-mod/i)*inv_[mod%i])%mod;
            fac_[i]=(fac_[i-1]*i)%mod;
            fac_inv_[i]=(fac_inv_[i-1]*inv_[i])%mod;
        }
    }
    long long inv(long long n){
        if(n<0)return 0;
        return inv_[n];
    }
    long long fac(long long n){
        if(n<0)return 0;
        return fac_[n];
    }
    long long finv(long long n){
        if(n<0)return 0;
        return fac_inv_[n];
    }
    long long nCr(long long n,long long r){
        if(n<r||n<0||r<0)return 0;
        return ((fac_[n]*fac_inv_[n-r])%mod*fac_inv_[r])%mod;
    }
    long long nPr(long long n,long long r){
        if(n<r||n<0||r<0)return 0;
        return (fac_[n]*fac_inv_[n-r])%mod;
    }
};

factional_prime<998244353,5000000> fp;

signed main(){
	int N,M;cin>>N>>M;

	vector<mint> P(M);
	
	rep(i,M){
		int a=M-N*i;
		int b=M-i;

		if(a<0)continue;

		rep(j,N+1){
			int c=b*j;
			if(c>a)break;

			P[i]+=mint(j%2?-1:1)*fp.nCr(N,j)*fp.nCr(a-c+N,N);
		}
	}

	for(auto&&e:P)cout<<e.val()<<" ";cout<<endl;

	mint ans=0;
	rng(i,1,M)ans+=P[i];

	ans/=P[0];

	cout<<ans.val()<<endl;
}