#include 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]; 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); } long long fact[100003], fact_inv[100003]; 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 pow_mod(int n, long long k) { long long N, ans = 1; for (N = n; k > 0; k >>= 1, N = N * N % Mod) if (k & 1) ans = ans * N % Mod; return ans; } int main() { int N, M; scanf("%d %d", &N, &M); int i, d = (N <= M)? N: M; for (i = 1, fact[0] = 1; i <= d + 1; i++) fact[i] = fact[i-1] * i % Mod; for (i = d, fact_inv[d+1] = div_mod(1, fact[d+1], Mod); i >= 0; i--) fact_inv[i] = fact_inv[i+1] * (i + 1) % Mod; int a[262144], b[262144], c[262144]; for (i = 0; i <= d; i++) { if (i % 2 == 0) a[i] = pow_mod(M * 2 - i, N); else a[i] = Mod - pow_mod(M * 2 - i, N); a[i] = a[i] * fact_inv[i] % Mod; b[i] = fact_inv[i]; } prod_polynomial(d, d, a, b, c); long long ans = 0; for (i = 1; i <= d; i++) ans += fact[i] * c[i] % Mod; printf("%lld\n", ans % Mod); fflush(stdout); return 0; }