#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
#define QWQ cout<<"QwQ"<<endl;
#define ll long long
#define poly vector<ll>
#include <vector>
#include <queue>
#include <stack>
#include <map>
using namespace std;
const ll N=101010;
const ll qwq=303030;
const ll inf=0x3f3f3f3f3f3f3f3f;
const ll p=998244353;

inline ll read() {
	ll sum = 0, f = 1; char c = getchar();
	while(c<'0' || c>'9') { if(c=='-') f = -1; c = getchar(); }
	while(c>='0'&&c<='9') { sum = sum * 10 + c - '0'; c = getchar(); }
	return sum * f;
}

ll n,K;
ll a[N],b[N];
poly ans;

ll f[N],ni[N];

inline ll ksm(ll aa,ll bb) {
    ll sum = 1;
    while(bb) {
        if(bb&1) sum = sum * aa %p;
        bb >>= 1; aa = aa * aa %p;
    }
    return sum;
}

inline ll CC(ll aa,ll bb) { return f[aa] * ni[bb] %p * ni[aa-bb] %p; }

void qiu() {
    f[0] = ni[0] = 1;
    for(ll i=1;i<=N-10;i++) f[i] = f[i-1] * i %p;
    ni[N-10] = ksm(f[N-10],p-2);
    for(ll i=N-11;i>=1;i--) ni[i] = ni[i+1] * (i+1) %p;
}

inline ll pipei(ll aa,ll bb,ll cc) {
	return CC(aa,cc) * CC(bb,cc) %p * f[cc] %p;
}

void outing(poly A) {
	for(ll v : A) cout<<v<<" ";
	cout<<endl;
}

poly DFS(ll la,ll ra,ll lb,ll rb,ll k) {
	// cout<<la<<","<<ra<<" "<<lb<<","<<rb<<" "<<k<<endl;
	// system("pause");
	poly res;
	if(la>ra || lb>rb) {
		res.resize(1);
		res[0] = 1;
		// outing(res);
		return res;
	}

	if(k==-1) {
		res.resize( min(ra-la+1, rb-lb+1)+1 );
		for(ll i=0;i<res.size();i++) res[i] = pipei(ra-la+1,rb-lb+1,i);
			// outing(res);
		return res;
	}

	ll l = la, r = ra, mid, mida = la-1, midb = lb-1;
	while(l<=r) {
		mid = l+r >> 1;
		if((a[mid]>>k)&1) r = mid-1;
		else mida = mid, l = mid+1;
	}
	l = lb, r = rb;
	while(l<=r) {
		mid = l+r >> 1;
		if((b[mid]>>k)&1) r = mid-1;
		else midb = mid, l = mid+1;
	}

	if((K>>k)&1) {
		poly A = DFS(la, mida, midb+1, rb, k-1);
		poly B = DFS(mida+1, ra, lb, midb, k-1);
		res.resize( A.size()+B.size()-1 );
		for(ll i=0;i<A.size();i++)
			for(ll j=0;j<B.size();j++)
				(res[i+j] += A[i] * B[j] %p) %= p;
			// outing(res);
		return res;
	}
	else {
		poly A = DFS(la, mida, lb, midb, k-1);
		poly B = DFS(mida+1, ra, midb+1, rb, k-1);
		res.resize( min(ra-la+1, rb-lb+1) + 1 );
		for(ll i=0;i<A.size();i++) {
			for(ll j=0;j<B.size();j++) {
				ll A0 = mida-la+1-i;
				ll B0 = midb-lb+1-i;
				ll A1 = ra-mida-j;
				ll B1 = rb-midb-j;
				for(ll x=0;x<=min(A0,B1);x++)
					for(ll y=0;y<=min(A1,B0);y++)
						(res[i+j+x+y] += A[i] * B[j] %p * pipei(A0,B1,x) %p * pipei(A1,B0,y) %p) %= p;
			}
		}
		// outing(res);
		return res;
	}
}

int main() {
	// freopen("data.in", "r", stdin);
	// freopen("K.in", "w", stdout);
	qiu();
	n = read(); K = read();
	for(ll i=1;i<=n;i++) a[i] = read();
	for(ll i=1;i<=n;i++) b[i] = read();
	sort(a+1,a+n+1);
	sort(b+1,b+n+1);
	ans = DFS(1,n,1,n,61);
	for(ll i=1;i<=n;i++) cout<<ans[i]<<"\n";
	return 0;
}

/*

9 5
1 2 2 4 5 7 8 9 10
1 2 3 4 5 8 8 8 9

*/