#include <bits/stdc++.h>
using namespace std;
constexpr int mod = 998244353, G = 3;
using poly = vector<int>;
constexpr int maxn = 1 << 18, N = maxn + 10;
int w[N], inv[N], lg[N], rev[N], invfac[N], fac[N];
int val;
inline int add(int a, int b) {return (a += b - mod), a += a >> 31 & mod;}
inline int sub(int a, int b) {return (a -= b), a += a >> 31 & mod;}
inline int fpw(int a, int b) {
	int ans = 1;
	for(; b; b >>= 1, a = 1ll * a * a % mod) if(b & 1) ans = 1ll * ans * a % mod;
	return ans;
}
void init() {
	inv[1] = 1;
	for(int i = 2; i < N; i ++) lg[i] = lg[i + 1 >> 1] + 1;
	for(int i = 2; i < N; i ++) inv[i] = 1ll * inv[mod % i] * (mod - mod / i) % mod;
	invfac[0] = fac[0] = 1;
	for(int i = 1; i < N; i ++) fac[i] = 1ll * fac[i - 1] * i % mod;
	for(int i = 1; i < N; i ++) invfac[i] = 1ll * invfac[i - 1] * inv[i] % mod;
	int wn = fpw(G, (mod - 1) / maxn); w[0] = 1;
	for(int i = 1; i < N; i ++) w[i] = 1ll * wn * w[i - 1] % mod;
}
void dft(poly &a, int len) {
	for(int i = len >> 1; i >= 1; i >>= 1) {
		int s = maxn / (i << 1);
		for(int j = 0; j < len; j += i << 1) {
			for(int k = 0, *p = w; k < i; k ++, p += s) {
				int x = a[j + k], y = a[i + j + k];
				a[j + k] = add(x, y);
				a[i + j + k] = 1ll * *p * sub(x, y) % mod;
			}
		}
	}
}
void idft(poly &a, int len) {
	for(int i = 1; i < len; i <<= 1) {
		int s = maxn / (i << 1);
		for(int j = 0; j < len; j += i << 1) {
			for(int k = 0, *p = w; k < i; k ++, p += s) {
				int x = a[j + k], y = 1ll * *p * a[i + j + k] % mod;
				a[j + k] = add(x, y);
				a[i + j + k] = sub(x, y);
			}
		}
	}
	reverse(a.begin() + 1, a.end());
	for(int &x : a) x = 1ll * x * inv[len] % mod;
}
poly polymul(poly a, poly b) {
	int len = a.size() + b.size() - 1, mxlen = 1 << lg[len];
	a.resize(mxlen), b.resize(mxlen);
	dft(a, mxlen), dft(b, mxlen);
	for(int i = 0; i < mxlen; i ++) a[i] = 1ll * a[i] * b[i] % mod;
	idft(a, mxlen), a.resize(len);
	return a;
}
poly polymulT(poly a, poly b) {
    int n = a.size(), m = b.size();
    reverse(b.begin(), b.end());
	int mxlen = 1 << lg[n];
	a.resize(mxlen), b.resize(mxlen);
	dft(a, mxlen), dft(b, mxlen);
	for(int i = 0; i < mxlen; i ++) a[i] = 1ll * a[i] * b[i] % mod;
	idft(a, mxlen);
	poly c(n - m + 1);
    for(int i = 0; i < n - m + 1; i ++) c[i] = a[i + m - 1];
	return c;
}
int n, m;
int a[N], b[N];
poly sum[N << 2];
#define ls u << 1 
#define rs u << 1 | 1
void dfs1(int u, int l, int r) {
	if(l == r) {
		sum[u].resize(b[l]);
		for(int i = 0; i < b[l]; i ++) {
			sum[u][i] = 1ll * invfac[i] * invfac[a[l] - i] % mod;
		}
		return ;
	}
	int mid = l + r >> 1;
	dfs1(ls, l, mid), dfs1(rs, mid + 1, r);
	sum[u] = polymul(sum[ls], sum[rs]);
}
void dfs2(int u, int l, int r, poly f) {
	if(l == r) {
		cout << 1ll * val * f[b[l] - 1] % mod * invfac[b[l] - 1] % mod * invfac[a[l] - b[l]] % mod << '\n';
	} else {
		int mid = l + r >> 1;
		dfs2(ls, l, mid, polymulT(f, sum[rs]));
		dfs2(rs, mid + 1, r, polymulT(f, sum[ls]));
	}
}
#undef ls 
#undef rs
int main() {
	// freopen("in.txt", "r", stdin);
	ios::sync_with_stdio(false), cin.tie(0);
	init();
	cin >> n >> m;
	val = 1;
	for(int i = 1; i <= n; i ++) {
		cin >> a[i];
		val = 1ll * val * fac[a[i]] % mod;
	}
	for(int i = 1; i <= n; i ++) {
		cin >> b[i];
	}
	dfs1(1, 1, n);
	poly f(m);
	for(int i = 0; i < m; i ++) {
		f[i] = 1ll * fac[i] * fac[m - i - 1] % mod;
	}
	dfs2(1, 1, n, f);
	return 0;
}