MOD = 998244353 IMAG = 911660635 IIMAG = 86583718 rate2 = ( 0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0, ) irate2 = ( 0, 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0, ) rate3 = ( 0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0, ) irate3 = ( 0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0, ) def butterfly(a): n = len(a) h = (n - 1).bit_length() le = 0 while le < h: if h - le == 1: p = 1 << (h - le - 1) rot = 1 for s in range(1 << le): offset = s << (h - le) for i in range(p): l = a[i + offset] r = a[i + offset + p] * rot a[i + offset] = (l + r) % MOD a[i + offset + p] = (l - r) % MOD rot *= rate2[(~s & -~s).bit_length()] rot %= MOD le += 1 else: p = 1 << (h - le - 2) rot = 1 for s in range(1 << le): rot2 = rot * rot % MOD rot3 = rot2 * rot % MOD offset = s << (h - le) for i in range(p): a0 = a[i + offset] a1 = a[i + offset + p] * rot a2 = a[i + offset + p * 2] * rot2 a3 = a[i + offset + p * 3] * rot3 a1na3imag = (a1 - a3) % MOD * IMAG a[i + offset] = (a0 + a2 + a1 + a3) % MOD a[i + offset + p] = (a0 + a2 - a1 - a3) % MOD a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % MOD a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % MOD rot *= rate3[(~s & -~s).bit_length()] rot %= MOD le += 2 def butterfly_inv(a): n = len(a) h = (n - 1).bit_length() le = h while le: if le == 1: p = 1 << (h - le) irot = 1 for s in range(1 << (le - 1)): offset = s << (h - le + 1) for i in range(p): l = a[i + offset] r = a[i + offset + p] a[i + offset] = (l + r) % MOD a[i + offset + p] = (l - r) * irot % MOD irot *= irate2[(~s & -~s).bit_length()] irot %= MOD le -= 1 else: p = 1 << (h - le) irot = 1 for s in range(1 << (le - 2)): irot2 = irot * irot % MOD irot3 = irot2 * irot % MOD offset = s << (h - le + 2) for i in range(p): a0 = a[i + offset] a1 = a[i + offset + p] a2 = a[i + offset + p * 2] a3 = a[i + offset + p * 3] a2na3iimag = (a2 - a3) * IIMAG % MOD a[i + offset] = (a0 + a1 + a2 + a3) % MOD a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % MOD a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % MOD a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % MOD irot *= irate3[(~s & -~s).bit_length()] irot %= MOD le -= 2 def multiply(s, t): n = len(s) m = len(t) if min(n, m) <= 60: a = [0] * (n + m - 1) for i in range(n): if i % 8 == 0: for j in range(m): a[i + j] += s[i] * t[j] a[i + j] %= MOD else: for j in range(m): a[i + j] += s[i] * t[j] return [x % MOD for x in a] a = s.copy() b = t.copy() z = 1 << (n + m - 2).bit_length() a += [0] * (z - n) b += [0] * (z - m) butterfly(a) butterfly(b) for i in range(z): a[i] *= b[i] a[i] %= MOD butterfly_inv(a) a = a[: n + m - 1] iz = pow(z, MOD - 2, MOD) return [v * iz % MOD for v in a] def main(): n, k = map(int, input().split()) fact = [1] * (10 * n) for i in range(1, len(fact)): fact[i] = fact[i - 1] * i % MOD inv_fact = [1] * (10 * n) inv_fact[-1] = pow(fact[-1], -1, MOD) for i in reversed(range(len(inv_fact) - 1)): inv_fact[i] = inv_fact[i + 1] * (i + 1) % MOD def comb(x, y): return fact[x] * inv_fact[y] * inv_fact[x - y] % MOD m = (n + 1) // 2 f = [0] * (10 * m + 1) for i in range(m + 1): tmp = comb(m, i) if i % 2 == 1: tmp = -tmp % MOD f[i * 10] = tmp g = [0] * (9 * m + 1) for i in range(len(g)): g[i] = comb(i + m - 1, i) h0 = multiply(f, g)[: 9 * m + 1] m = n // 2 f = [0] * (10 * m + 1) for i in range(m + 1): tmp = comb(m, i) if i % 2 == 1: tmp = -tmp % MOD f[i * 10] = tmp g = [0] * (9 * m + 1) for i in range(len(g)): g[i] = comb(i + m - 1, i) h1 = multiply(f, g)[: 9 * m + 1] ans = 0 for d in range(11): f = [0] * len(h0) f[d::11] = h0[d::11] g = [0] * len(h1) g[d::11] = h1[d::11] h = multiply(f, g) for i in range(0, len(h), 9): ans += pow(i, k, MOD) * h[i] % MOD if ans >= MOD: ans -= MOD print(ans) if __name__ == "__main__": main()