mod = 998244353 def main(): import sys input = sys.stdin.readline W = ( 1, 998244352, 911660635, 372528824, 929031873, 452798380, 922799308, 781712469, 476477967, 166035806, 258648936, 584193783, 63912897, 350007156, 666702199, 968855178, 629671588, 24514907, 996173970, 363395222, 565042129, 733596141, 267099868, 15311432) IW = (1, 998244352, 86583718, 509520358, 337190230, 87557064, 609441965, 135236158, 304459705, 685443576, 381598368, 335559352, 129292727, 358024708, 814576206, 708402881, 283043518, 3707709, 121392023, 704923114, 950391366, 428961804, 382752275, 469870224) # A: 係数を並べたベクトル,len(A) = 2^n def fft(A): N = len(A) n = N.bit_length() - 1 N2 = N // 2 A_new = [0] * N for lv in range(n): L = 1 << (n - lv - 1) w = W[lv + 1] ww = 1 for j in range(1 << lv): for i in range(L): f0_val = A[i + j * L * 2] f1_val = A[i + j * L * 2 + L] tmp = (ww * f1_val) % mod A_new[i + j * L] = (f0_val + tmp) % mod A_new[i + j * L + N2] = (f0_val - tmp) % mod ww = (ww * w) % mod A, A_new = A_new, A return A # A: 係数を並べたベクトル,len(A) = 2^n def ifft(A): N = len(A) n = N.bit_length() - 1 N2 = N // 2 A_new = [0] * N for lv in range(n): L = 1 << (n - lv - 1) w = IW[lv + 1] ww = 1 for j in range(1 << lv): for i in range(L): f0_val = A[i + j * L * 2] f1_val = A[i + j * L * 2 + L] tmp = (ww * f1_val) % mod A_new[i + j * L] = (f0_val + tmp) % mod A_new[i + j * L + N2] = (f0_val - tmp) % mod ww = (ww * w) % mod A, A_new = A_new, A return A def convolution(A0, B0, limit): if len(A0) <= 60 or len(B0) <= 60: return convolution_naive(A0, B0, limit) N = len(A0) + len(B0) - 1 N0 = 1 << ((N - 1).bit_length()) A = A0 + [0] * (N0 - len(A0)) B = B0 + [0] * (N0 - len(B0)) AA = fft(A) BB = fft(B) CC = [(aa * bb) % mod for aa, bb in zip(AA, BB)] C = ifft(CC) invN0 = pow(N0, mod - 2, mod) C = [(c * invN0) % mod for c in C] return C[:limit] def convolution_naive(A0, B0, limit): NA = len(A0) NB = len(B0) C = [0] * (NA + NB - 1) for i in range(NA): for j in range(NB): C[i + j] = (C[i + j] + (A0[i] * B0[j]) % mod) % mod return C[:limit] # comb init nmax = 2 * 10 ** 3 + 10 # change here fac = [0] * nmax finv = [0] * nmax inv = [0] * nmax fac[0] = 1 fac[1] = 1 finv[0] = 1 finv[1] = 1 inv[1] = 1 for i in range(2, nmax): fac[i] = fac[i - 1] * i % mod inv[i] = mod - inv[mod % i] * (mod // i) % mod finv[i] = finv[i - 1] * inv[i] % mod def comb(n, r): if n < r: return 0 else: return (fac[n] * ((finv[r] * finv[n - r]) % mod)) % mod N, M = map(int, input().split()) vec = [] for i in range(N+1): vec.append(((pow(2, i, mod) - 1) * finv[i])%mod) dp = [vec[:]] for i in range(1, min(N, M + 1)): dp.append(convolution(vec, dp[-1], N+1)) vec.pop() ans = 0 for i in range(min(N, M + 1)): powM = 1 pow2 = 1 for j in range(N, -1, -1): if i == M: if j == N: ans = (ans + dp[i][j])%mod else: ans = (ans + ((dp[i][j] * powM)%mod * (finv[N - j] * pow2)%mod)%mod)%mod powM = (powM * (M - i))%mod pow2 = (pow2 * 2)%mod print((ans * fac[N])%mod) if __name__ == '__main__': main()