#include long long mod_num = 998244353LL; long long root = 3LL; int length = 998244352; long long inverse_root = 0LL; long long inverse_l = 0LL; 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 = 2; while(tmp_length < 2*l) { tmp_length *= 2; } 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; return; } void ntt_2n (long long *a, long long root) { int log = 0; long long pow_root[32] = {}; while ((1< 0; i--) { pow_root[i-1] = pow_root[i]; pow_root[i-1] *= pow_root[i]; pow_root[i-1] %= mod_num; } for (int i = 0; i < length; i++) { int idx = 0; int tmp = i; for (int j = 0; j < log; j++) { idx <<= 1; idx |= (tmp&1); tmp >>= 1; } if (i < idx) { int swap = a[i]; a[i] = a[idx]; a[idx] = swap; } } for (int i = 0; i < log; i++) { int step = (1< 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_2n(work[1], 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_2n(work[0], root); for (int j = 0; j < length; j++) { work[0][j] *= work[1][j]; work[0][j] %= mod_num; } ntt_2n(work[0], inverse_root); for (int j = 0; j <= l; j++) { work[0][j] *= inverse_l; work[0][j] %= mod_num; work[1][j] = work[0][j]; } for (int j = l+1; j < length; j++) { work[0][j] = 0LL; work[1][j] = 0LL; } ntt_2n(work[1], 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_2n(ans, root); for (int i = 0; i < length; i++) { ans[i] *= work[1][i]; ans[i] %= mod_num; } ntt_2n(ans, inverse_root); for (int i = 0; i <= l; i++) { ans[i] *= inverse_l; ans[i] %= mod_num; } } m /= 2; } for (int i = 0; i < l; i++) { printf("%lld\n", (ans[i+1]*fact[i+1])%mod_num); } return 0; }