def mul_poly(f,g): df,dg = len(f),len(g) res = [0]*(df+dg-1) for i in range(df): for j in range(dg): res[i+j] += f[i]*g[j] res[i+j] %= MOD return res def sub_poly(f,g): df,dg = len(f),len(g) m = max(df,dg) res = f[:]+[0]*max(0,m-df) for i in range(m): if i < dg: res[i] -= g[i] if res[i] < 0: res[i] += MOD return res def divmod_poly(f,g): assert g != [] and g != [0] ginv = pow(g[-1],MOD-2,MOD) df,dg = len(f),len(g) if df < dg: return [0], f[:] gg = [gi*ginv%MOD for gi in g] r = f[:] for i in range(df-dg,-1,-1): for j in range(dg-2,-1,-1): r[j+i] -= r[dg+i-1]*gg[j] r[j+i] %= MOD q = r[dg-1:] r = r[:dg-1] for i in range(df-dg+1): # g を monic にする q[i] = q[i]*ginv%MOD while r and r[-1]==0: r.pop() if not r: r = [0] return q,r """ 数列 f の最小の線形漸化式を発見する f = r/q (mod X^N) の形で返す """ def find_linear_reccurence(f): r0 = [0]*len(f)+[1] r1 = f[:] while r1 and r1[-1]==0: r1.pop() if not r1: return [0],[0] # all 0 なら 0 が解 q0,q1 = [0],[1] r_ans, q_ans, size_ans = r1, q1, len(r1)+1 while r1 != [0]: q,r = divmod_poly(r0,r1) r0,r1 = r1,r q0,q1 = q1,sub_poly(q0,mul_poly(q,q1)) size = max(len(q1),len(r1)+1) if q1[0] and size < size_ans: r_ans, q_ans, size_ans = r1, q1, size if len(q_ans) <= len(r_ans): q_ans += [0]*(len(r_ans)-len(q_ans)+1) qinv = pow(q_ans[0],MOD-2,MOD) for i in range(len(q_ans)): q_ans[i] = q_ans[i]*qinv%MOD for i in range(len(r_ans)): r_ans[i] = r_ans[i]*qinv%MOD return r_ans, q_ans def polymul(f,g): lf = len(f) lg = len(g) res = [0]*(lf+lg-1) for i in range(lf): for j in range(lg): res[i+j] += f[i]*g[j] res[i+j] %= MOD return res def fps_nth_term(f,g,N): assert g[0] != 0 while N: h = g[:] for i in range(1,len(g),2): h[i] = -h[i] f = polymul(f,h)[N%2:N+1:2] g = polymul(g,h)[:N+1:2] N //= 2 return f[0]*pow(g[0],MOD-2,MOD)%MOD n,k = map(int,input().split()) MOD = 998244353 dpn = [[0]*k for _ in range(k)] dps = [[0]*k for _ in range(k)] for i in range(k): for j in range(i+1,k): dpn[i][j] = dpn[j][i] = 1 dps[i][j] = dps[j][i] = i+j M = 100 vn = [0]*M vs = [0]*M for I in range(M): ndpn = [[0]*k for _ in range(k)] ndps = [[0]*k for _ in range(k)] for i in range(k): for j in range(k): if ij: for p in range(j+1,k): if i==p: continue ndpn[j][p] += dpn[i][j] ndpn[j][p] %= MOD ndps[j][p] += dps[i][j] + dpn[i][j]*p ndps[j][p] %= MOD dpn = ndpn dps = ndps vn[I] = sum(sum(i) for i in dpn)%MOD vs[I] = sum(sum(i) for i in dps)%MOD r,q = find_linear_reccurence(vn) print(fps_nth_term(r,q,n-3), end=" ") r,q = find_linear_reccurence(vs) print(fps_nth_term(r,q,n-3))