MOD = 998244353 def main(): import sys input = sys.stdin.read().split() N = int(input[0]) K = int(input[1]) if N < 3: print(0, 0) return # Initialize for i=2 prev_count = [[0] * K for _ in range(K)] prev_sum = [[0] * K for _ in range(K)] for a in range(K): for b in range(K): if a != b: prev_count[a][b] = 1 prev_sum[a][b] = a + b for i in range(3, N + 1): current_count = [[0] * K for _ in range(K)] current_sum = [[0] * K for _ in range(K)] # Precompute prefix sums for each b_prev prefix_count = [[0] * K for _ in range(K)] prefix_sum = [[0] * K for _ in range(K)] for b_prev in range(K): # Compute prefix_count[b_prev][x] prefix_count[b_prev][0] = prev_count[0][b_prev] prefix_sum[b_prev][0] = prev_sum[0][b_prev] for x in range(1, K): prefix_count[b_prev][x] = (prefix_count[b_prev][x-1] + prev_count[x][b_prev]) % MOD prefix_sum[b_prev][x] = (prefix_sum[b_prev][x-1] + prev_sum[x][b_prev]) % MOD # Iterate over all (b_prev, c) for b_prev in range(K): for c in range(K): if b_prev == c: continue sum_count = 0 sum_sum = 0 if b_prev > c: # a_prev in 0..b_prev-1, exclude c if b_prev == 0: sum_count = 0 sum_sum = 0 else: sum_count = prefix_count[b_prev][b_prev - 1] sum_sum = prefix_sum[b_prev][b_prev - 1] # Subtract if c is within the range if c < b_prev: sum_count = (sum_count - prev_count[c][b_prev]) % MOD sum_sum = (sum_sum - prev_sum[c][b_prev]) % MOD else: # b_prev < c: a_prev in b_prev+1..K-1, exclude c if b_prev + 1 >= K: sum_count = 0 sum_sum = 0 else: sum_count = (prefix_count[b_prev][K-1] - prefix_count[b_prev][b_prev]) % MOD sum_sum = (prefix_sum[b_prev][K-1] - prefix_sum[b_prev][b_prev]) % MOD # Subtract if c is in the range if c >= b_prev + 1 and c < K: sum_count = (sum_count - prev_count[c][b_prev]) % MOD sum_sum = (sum_sum - prev_sum[c][b_prev]) % MOD # Update current_count and current_sum current_count[b_prev][c] = (current_count[b_prev][c] + sum_count) % MOD current_sum[b_prev][c] = (current_sum[b_prev][c] + (sum_sum + sum_count * c) % MOD) % MOD # Update prev_count and prev_sum for next iteration prev_count, prev_sum = current_count, current_sum ans_1 = 0 ans_2 = 0 for a in range(K): for b in range(K): ans_1 = (ans_1 + prev_count[a][b]) % MOD ans_2 = (ans_2 + prev_sum[a][b]) % MOD print(ans_1, ans_2) if __name__ == "__main__": main()