import sys from collections import defaultdict, Counter, deque from itertools import permutations, combinations, product, combinations_with_replacement, groupby, accumulate import operator from math import sqrt, gcd, factorial # from math import isqrt, prod,comb # python3.8用(notpypy) #from bisect import bisect_left,bisect_right #from functools import lru_cache,reduce #from heapq import heappush,heappop,heapify,heappushpop,heapreplace #import numpy as np #import networkx as nx #from networkx.utils import UnionFind #from numba import njit, b1, i1, i4, i8, f8 #from scipy.sparse import csr_matrix #from scipy.sparse.csgraph import shortest_path, floyd_warshall, dijkstra, bellman_ford, johnson, NegativeCycleError # numba例 @njit(i1(i4[:], i8[:, :]),cache=True) 引数i4配列、i8 2次元配列,戻り値i1 def input(): return sys.stdin.readline().rstrip() def divceil(n, k): return 1+(n-1)//k # n/kの切り上げを返す def yn(hantei, yes='Yes', no='No'): print(yes if hantei else no) def calc(a1, a2, b1, b2, k, mod): c1 = [0]*k**4 c2 = [0]*k**4 for a, b, c, d, e, f in product(range(k), repeat=6): c1[a*k**3+b*k**2+e*k+f] += a1[a*k**3 + b*k**2+c*k+d]*b1[c*k**3+d*k**2+e*k+f] c2[a*k**3+b*k**2+e*k+f] += a1[a*k**3+b*k**2+c*k+d] * \ b2[c*k**3+d*k**2+e*k+f]+a2[a*k**3+b * k**2+c*k+d]*b1[c*k**3+d*k**2+e*k+f] c1[a*k**3+b*k**2+e*k+f] %= mod c2[a*k**3+b*k**2+e*k+f] %= mod return c1, c2 def check(a): return a[0] != a[1] and a[1] != a[2] and a[2] != a[0] and a[1] in [max(a), min(a)] def main(): mod = 10**9+7 mod2 = 998244353 n, k = map(int, input().split()) assert 3 <= n <= 10**9, 3 <= k <= 9 a1 = [0]*k**4 a2 = [0]*k**4 for w, y, z in product(range(k), repeat=3): if check((w, y, z)): a1[w*k**3+y*k**2+y*k+z] = 1 a2[w*k**3+y*k**2+y*k+z] = z ans1 = None ans2 = None n -= 2 while n: n, i = divmod(n, 2) if i: if ans1: ans1, ans2 = calc(ans1, ans2, a1, a2, k, mod2) else: ans1, ans2 = a1[:], a2[:] a1, a2 = calc(a1, a2, a1, a2, k, mod2) sumans1 = sum(ans1) sumans2 = 0 for w, x, y, z in product(range(k), repeat=4): sumans2 += ans1[w*k**3+x*k**2+y*k+z]*(w+x)+ans2[w*k**3+x*k**2+y*k+z] print(sumans1 % mod2, sumans2 % mod2) if __name__ == '__main__': main()