_fft_mod = 998244353 _fft_sum_e = [911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 0, 0, 0, 0, 0, 0, 0, 0, 0] _fft_sum_ie = [86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 0, 0, 0, 0, 0, 0, 0, 0, 0] def butterfly_998244353(a): n = len(a) h = (n - 1).bit_length() for ph in range(1, h + 1): w = 1 << (ph - 1) p = 1 << (h - ph) now = 1 for s in range(w): offset = s << (h - ph + 1) for i in range(p): l = a[i + offset] r = a[i + offset + p] * now % _fft_mod a[i + offset] = (l + r) % _fft_mod a[i + offset + p] = (l - r) % _fft_mod now = now * _fft_sum_e[(~s & -~s).bit_length() - 1] % _fft_mod def butterfly_inv_998244353(a): n = len(a) h = (n - 1).bit_length() for ph in range(h, 0, -1): w = 1 << (ph - 1) p = 1 << (h - ph) inow = 1 for s in range(w): offset = s << (h - ph + 1) for i in range(p): l = a[i + offset] r = a[i + offset + p] a[i + offset] = (l + r) % _fft_mod a[i + offset + p] = (l - r) * inow % _fft_mod inow = inow * _fft_sum_ie[(~s & -~s).bit_length() - 1] % _fft_mod def convolution_998244353(a, b): a = a.copy() b = b.copy() n = len(a) m = len(b) if n == 0 or m == 0: return [] if min(n, m) <= 60: if n < m: n, m = m, n a, b = b, a ans = [0] * (n + m - 1) for i in range(n): for j in range(m): ans[i + j] = (ans[i + j] + a[i] * b[j] % _fft_mod) % _fft_mod return ans z = 1 << (n + m - 2).bit_length() a += [0] * (z - n) b += [0] * (z - m) butterfly_998244353(a) butterfly_998244353(b) for i in range(z): a[i] = a[i] * b[i] % _fft_mod butterfly_inv_998244353(a) a = a[:n + m - 1] iz = pow(z, _fft_mod - 2, _fft_mod) for i in range(n + m - 1): a[i] = a[i] * iz % _fft_mod return a mod=998244353 def cmb(n,r): if r<0 or r>n: return 0 return (g1[n]*g2[r]*g2[n-r])%mod g1=[1,1] g2=[1,1] inv=[0,1] for i in range(2,1000003): g1.append((g1[-1]*i)%mod) inv.append((-inv[mod%i]*(mod//i))%mod) g2.append((g2[-1]*inv[-1])%mod) g2.append(1) G=[1,1] for i in range(1,1000003): G.append((G[-1]*i+1)%mod) def psum(N,K): if N