#include <stdio.h>
#include <stdlib.h>

const int Mod = 998244353,
	bit[21] = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576},
	bit_inv[21] = {1, 499122177, 748683265, 873463809, 935854081, 967049217, 982646785, 990445569, 994344961, 996294657, 997269505, 997756929, 998000641, 998122497, 998183425, 998213889, 998229121, 998236737, 998240545, 998242449, 998243401},
	root[21] = {1, 998244352, 911660635, 372528824, 929031873, 452798380, 922799308, 781712469, 476477967, 166035806, 258648936, 584193783, 63912897, 350007156, 666702199, 968855178, 629671588, 24514907, 996173970, 363395222, 565042129},
	root_inv[21] = {1, 998244352, 86583718, 509520358, 337190230, 87557064, 609441965, 135236158, 304459705, 685443576, 381598368, 335559352, 129292727, 358024708, 814576206, 708402881, 283043518, 3707709, 121392023, 704923114, 950391366};
int ntt_b[21][1048576], ntt_c[21][1048576], ntt_x[21][1048576], ntt_y[21][1048576];

long long div_mod(long long x, long long y, long long z)
{
	if (x % y == 0) return x / y;
	else return (div_mod((1 + x / y) * y - x, (z % y), y) * z + x) / y;
}

void NTT(int k, int a[], int z[])
{
	if (k == 0) {
		z[0] = a[0];
		return;
	}
	
	int i, d = bit[k-1], tmpp;
	long long tmp;
	for (i = 0; i < d; i++) {
		ntt_b[k][i] = a[i*2];
		ntt_c[k][i] = a[i*2+1];
	}
	NTT(k - 1, ntt_b[k], ntt_x[k]);
	NTT(k - 1, ntt_c[k], ntt_y[k]);
	for (i = 0, tmp = 1; i < d; i++, tmp = tmp * root[k] % Mod) {
		tmpp = tmp * ntt_y[k][i] % Mod;
		z[i] = ntt_x[k][i] + tmpp;
		if (z[i] >= Mod) z[i] -= Mod;
		z[i+d] = ntt_x[k][i] - tmpp;
		if (z[i+d] < 0) z[i+d] += Mod;
	}
}

void NTT_reverse(int k, int z[], int a[])
{
	if (k == 0) {
		a[0] = z[0];
		return;
	}
	
	int i, d = bit[k-1], tmpp;
	long long tmp;
	for (i = 0; i < d; i++) {
		ntt_x[k][i] = z[i*2];
		ntt_y[k][i] = z[i*2+1];
	}
	NTT_reverse(k - 1, ntt_x[k], ntt_b[k]);
	NTT_reverse(k - 1, ntt_y[k], ntt_c[k]);
	for (i = 0, tmp = 1; i < d; i++, tmp = tmp * root_inv[k] % Mod) {
		tmpp = tmp * ntt_c[k][i] % Mod;
		a[i] = ntt_b[k][i] + tmpp;
		if (a[i] >= Mod) a[i] -= Mod;
		a[i+d] = ntt_b[k][i] - tmpp;
		if (a[i+d] < 0) a[i+d] += Mod;
	}
}
// Compute the product of two polynomials a[0-da] and b[0-db] using NTT in O(d * log d) time
void prod_poly_NTT(int da, int db, int a[], int b[], int c[])
{
	int i, k;
	static int aa[1048576], bb[1048576], cc[1048576];
	for (k = 0; bit[k] <= da + db; k++);
	for (i = 0; i <= da; i++) aa[i] = a[i];
	for (i = da + 1; i < bit[k]; i++) aa[i] = 0;
	for (i = 0; i <= db; i++) bb[i] = b[i];
	for (i = db + 1; i < bit[k]; i++) bb[i] = 0;
	
	static int x[1048576], y[1048576], z[1048576];
	NTT(k, aa, x);
	if (db == da) {
		for (i = 0; i <= da; i++) if (a[i] != b[i]) break;
		if (i <= da) NTT(k, bb, y);
		else for (i = 0; i < bit[k]; i++) y[i] = x[i];
	} else NTT(k, bb, y);
	for (i = 0; i < bit[k]; i++) z[i] = (long long)x[i] * y[i] % Mod;
	NTT_reverse(k, z, cc);
	for (i = 0; i <= da + db; i++) c[i] = (long long)cc[i] * bit_inv[k] % Mod;
}

// Compute the product of two polynomials a[0-da] and b[0-db] naively in O(da * db) time
void prod_poly_naive(int da, int db, int a[], int b[], int c[])
{
	int i, j;
	for (i = 0; i <= da + db; i++) c[i] = 0;
	for (i = 0; i <= da; i++) {
		for (j = 0; j <= db; j++) {
			c[i+j] += (long long)a[i] * b[j] % Mod;
			if (c[i+j] >= Mod) c[i+j] -= Mod;
		}
	}
}

// Compute the product of two polynomials a[0-da] and b[0-db] in an appropriate way
void prod_polynomial(int da, int db, int a[], int b[], int c[])
{
	const int THR = 250000;
	if (THR / (da + 1) >= db + 1) prod_poly_naive(da, db, a, b, c);
	else prod_poly_NTT(da, db, a, b, c);
}

typedef struct Edge {
	struct Edge *next;
	int v;
} edge;

int main()
{
	int i, N, A[200001], par[200001], u, w;
	long long K;
	edge *adj[200001] = {}, e[200001], *p;
	scanf("%d %lld", &N, &K);
	for (i = 0; i <= N; i++) scanf("%d", &(A[i]));
	for (i = 1, par[0] = -1; i <= N; i++) {
		scanf("%d", &(par[i]));
		u = par[i];
		w = i;
		e[i].v = w;
		e[i].next = adj[u];
		adj[u] = &(e[i]);
	}
	
	int q[200001], head, tail, depth[200001], height[200001], hv_par[200001], hv_child[200001], hv_height[200001], hv_root[200001], *hv_path[200001], *hv_count[200001], max, argmax;
	q[0] = 0;
	depth[0] = 0;
	for (head = 0, tail = 1; head < tail; head++) {
		u = q[head];
		for (p = adj[u]; p != NULL; p = p->next) {
			w = p->v;
			depth[w] = depth[u] + 1;
			q[tail++] = w;
		}
	}
	for (head--; head >= 0; head--) {
		u = q[head];
		for (p = adj[u], max = 0; p != NULL; p = p->next) {
			w = p->v;
			if (max < height[w] + 1) {
				max = height[w] + 1;
				argmax = w;
			}
		}
		height[u] = max;
		if (max > 0) {
			hv_par[argmax] = u;
			hv_child[u] = argmax;
			hv_height[u] = hv_height[argmax] + 1;
		} else {
			hv_child[u] = -1;
			hv_height[u] = 0;
		}
		hv_par[u] = -1;
	}
	for (u = 0; u <= N; u++) {
		if (hv_par[u] >= 0) continue;
		hv_path[u] = (int*)malloc(sizeof(int) * (hv_height[u] + 1));
		hv_count[u] = (int*)malloc(sizeof(int) * (hv_height[u] + 1));
		for (w = u, i = hv_height[u]; w >= 0; w = hv_child[w], i--) {
			hv_path[u][i] = w;
			hv_root[w] = u;
		}
	}
	
	int a[400003], b[400003], c[400003];
	long long tmp = 1;
	for (i = 1, b[0] = 1; i <= N; i++) {
		if ((K - i + 1) % Mod == 0) tmp = 0;
		else tmp = tmp * ((K - i + 1) % Mod) % Mod;
		tmp = div_mod(tmp, i, Mod);
		b[i] = tmp;
	}
	
	int j, uu, ww;
	long long ans[200001] = {};
	for (head = tail - 1; head >= 0; head--) {
		u = q[head];
		w = hv_root[u];
		i = hv_height[u];
		hv_count[w][i] += A[u];
		if (hv_count[w][i] >= Mod) hv_count[w][i] -= Mod;
		if (hv_par[u] >= 0) continue;
		
		for (i = 0; i <= hv_height[w]; i++) a[i] = hv_count[w][i];
		prod_polynomial(hv_height[w], hv_height[w], a, b, c);
		for (i = 0; i <= hv_height[w]; i++) ans[hv_path[w][i]] += c[i];
		
		uu = par[w];
		if (uu < 0) continue;
		ww = hv_root[uu];
		for (i = 0, j = hv_height[uu] - hv_height[w] - 1; i <= hv_height[w]; i++, j++) {
			hv_count[ww][j] += hv_count[w][i];
			if (hv_count[ww][j] >= Mod) hv_count[ww][j] -= Mod;
			ans[hv_path[ww][j]] += Mod - c[i];
		}
	}
	for (u = 0; u <= N; u++) printf("%lld\n", ans[u] % Mod);
	fflush(stdout);
	return 0;
}