#include long long mod_num = 998244353LL; long long root = 3LL; int length = 998244352; long long inverse_root = 0LL; long long inverse_l = 0LL; int log_l = 0; long long pow_root[16] = {}; long long pow_root_inv[16] = {}; long long power_mod (long long a, long long b, long long p) { long long ans = 0LL; a %= p; if (b <= 0LL) { return 1LL; } ans = power_mod(a, b/2LL, p); ans = (ans * ans) % p; if (b%2LL == 1LL) { ans = (ans * a) % p; } return ans; } void setup_ntt (int l) { int tmp_length = 4; log_l = 1; while(tmp_length < 2*l) { tmp_length *= 4; log_l++; } root = power_mod(root, length / tmp_length, mod_num); inverse_root = power_mod(root, mod_num-2LL, mod_num); inverse_l = power_mod((long long) tmp_length, mod_num-2LL, mod_num); length = tmp_length; pow_root[log_l-1] = root; for (int i = log_l-1; i > 0; i--) { pow_root[i-1] = pow_root[i]; pow_root[i-1] *= pow_root[i]; pow_root[i-1] %= mod_num; pow_root[i-1] *= pow_root[i-1]; pow_root[i-1] %= mod_num; } pow_root_inv[log_l-1] = inverse_root; for (int i = log_l-1; i > 0; i--) { pow_root_inv[i-1] = pow_root_inv[i]; pow_root_inv[i-1] *= pow_root_inv[i]; pow_root_inv[i-1] %= mod_num; pow_root_inv[i-1] *= pow_root_inv[i-1]; pow_root_inv[i-1] %= mod_num; } return; } void ntt_4n (long long *a, long long *pow_root) { long long root_1_4 = pow_root[0]; for (int i = 0; i < length; i++) { int idx = 0; int tmp = i; for (int j = 0; j < log_l; j++) { idx <<= 2; idx |= (tmp&3); tmp >>= 2; } if (i < idx) { long long swap = a[i]; a[i] = a[idx]; a[idx] = swap; } } for (int i = 0; i < log_l; i++) { int ix2 = 2*i; int ix2_2 = ix2+2; int step = (1<>ix2_2; long long tmp_root = 1LL; for (int j = 0; j < step; j++) { long long w1 = tmp_root; long long w2 = (w1*w1)%mod_num; long long w3 = (w2*w1)%mod_num; for (int k = 0; k < cnt; k++) { int idx1 = ((k< 0; i--) { invf[i-1] = invf[i]; invf[i-1] *= (long long)i; invf[i-1] %= mod_num; } setup_ntt(l+1); work[0][0] = power_mod(2LL, (long long)n, mod_num); for (int i = 1; i <= l; i++) { work[0][i] = invf[i]; } for (int i = 0; i <= l; i++) { work[1][i] = work[0][i]; } ntt_4n(work[1], pow_root); if (m%2 == 1) { for (int i = 0; i <= l; i++) { ans[i] = work[0][i]; } } else { ans[0] = 1LL; } m /= 2; while (m > 0) { long long p = 1LL; for (int j = 0; j <= l; j++) { work[0][j] *= p; work[0][j] %= mod_num; p = (p*pow2)%mod_num; } ntt_4n(work[0], pow_root); for (int j = 0; j < length; j++) { work[0][j] *= work[1][j]; work[0][j] %= mod_num; } ntt_4n(work[0], pow_root_inv); for (int j = 0; j <= l; j++) { work[1][j] = work[0][j]; } for (int j = l+1; j < length; j++) { work[0][j] = 0LL; work[1][j] = 0LL; } pow_cnt = 2LL*pow_cnt+1LL; ntt_4n(work[1], pow_root); pow2 = (pow2*pow2)%mod_num; if (m%2 == 1) { long long p = 1LL; for (int i = 0; i <= l; i++) { ans[i] *= p; ans[i] %= mod_num; p = (p*pow2)%mod_num; } for (int i = l+1; i < length; i++) { ans[i] = 0LL; } ntt_4n(ans, pow_root); for (int i = 0; i < length; i++) { ans[i] *= work[1][i]; ans[i] %= mod_num; } ntt_4n(ans, pow_root_inv); inv_cnt += pow_cnt+1LL; } m /= 2; } pow_inv_l = power_mod(inverse_l, inv_cnt, mod_num); for (int i = 0; i < l; i++) { printf("%lld\n", (((ans[i+1]*pow_inv_l)%mod_num)*fact[i+1])%mod_num); } return 0; }