#include <stdio.h>

const int Mod = 998244353;
long long fact[3001], fact_inv[3001];

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;
}

long long combination(int n, int k)
{
	if (n < k) return 0;
	return fact[n] * fact_inv[k] % Mod * fact_inv[n-k] % Mod;
}

int main()
{
	int i, N, L, A[3002];
	scanf("%d %d", &N, &L);
	L = L * 2 + 1;
	for (i = 1, A[0] = 0, A[N+1] = L; i <= N; i++) {
		scanf("%d", &(A[i]));
		A[i] = A[i] * 2 + 1;
	}
	for (i = 1, fact[0] = 1; i <= N; i++) fact[i] = fact[i-1] * i % Mod;
	for (i = N - 1, fact_inv[N] = div_mod(1, fact[N], Mod); i >= 0; i--) fact_inv[i] = fact_inv[i+1] * (i + 1) % Mod;

	int j, k;
	long long ans[3001] = {};
	for (i = 1; i <= N; i++) {
		for (j = i + 1; j <= N; j++) if (A[j] > L - A[i]) break;
		k = j - i - 1;
		if (L - A[i] > A[i-1]) ans[i]++;
		for (j = i + 1; j <= N; j++) ans[j] += combination(k, j - i);
		
		for (j = i - 1; j >= 1; j--) if (L - A[j] > A[i]) break;
		k = i - j - 1;
		if (A[i] > L - A[i+1]) ans[i]++;
		for (j = i - 1; j >= 1; j--) ans[j] += combination(k, i - j);
	}
	for (i = 1; i <= N; i++) printf("%lld\n", ans[i] % Mod);
	fflush(stdout);
	return 0;
}