MOD = 10**9 + 9 inv3 = pow(3, MOD-2, MOD) inv6 = pow(6, MOD-2, MOD) def main(): import sys input = sys.stdin.read data = input().split() idx = 0 N = int(data[idx]) idx +=1 K = int(data[idx]) idx +=1 A = list(map(int, data[idx:idx+N])) if K == 0: sum_A = sum(a % MOD for a in A) % MOD part1_val = sum( (a * a) % MOD for a in A ) % MOD sum_part = (sum_A * sum_A - part1_val) % MOD part2_val = sum_part % MOD total_S2_over_x = (part1_val + part2_val) % MOD sigma_sq_4k = (total_S2_over_x * 1 - sum_A * sum_A) % MOD if sigma_sq_4k < 0: sigma_sq_4k += MOD print(sum_A % MOD) print(sigma_sq_4k % MOD) return # Compute mu_part pow_2k_minus_1 = (pow(2, K, MOD) - 1) % MOD pow_2k_1 = pow(2, K-1, MOD) mu_part = (N * pow_2k_1 % MOD) * pow_2k_minus_1 % MOD # Compute part1_val t1 = (pow(2, K, MOD) -1) % MOD t2 = pow(2, K, MOD) % MOD t3 = (pow(2, K+1, MOD) -1) % MOD sum_ysquared = t1 * t2 % MOD sum_ysquared = sum_ysquared * t3 % MOD sum_ysquared = sum_ysquared * inv6 % MOD part1_val = sum_ysquared * N % MOD # Compute same_part same_sum = 0 for b in range(K): cnt = 0 for a in A: if (a >> b) & 1: cnt +=1 cnt %= MOD c = cnt term1 = (c * (c-1)) // 2 % MOD nc = (N - c) % MOD term2 = (nc * (nc-1)) // 2 % MOD equal_pairs = (term1 + term2) % MOD power_4b = pow(4, b, MOD) same_sum = (same_sum + equal_pairs * power_4b) % MOD pow_2k_1 = pow(2, K-1, MOD) same_part = same_sum * pow_2k_1 % MOD # Compute different_part term = (pow(2, K, MOD) -1) % MOD term = term * term % MOD term2 = (pow(4, K, MOD) -1) % MOD term2 = term2 * inv3 % MOD term_diff = (term - term2) % MOD if term_diff < 0: term_diff += MOD term_diff = term_diff * pow(2, K-2, MOD) % MOD c_n_2 = (N * (N-1) // 2) % MOD different_part = term_diff * c_n_2 % MOD part2_val = (2 * (same_part + different_part)) % MOD total_S2_over_x = (part1_val + part2_val) % MOD sigma_sq_4k = (total_S2_over_x * pow(2, K, MOD) % MOD) - (mu_part * mu_part % MOD) sigma_sq_4k %= MOD if sigma_sq_4k <0: sigma_sq_4k += MOD print(mu_part % MOD) print(sigma_sq_4k % MOD) if __name__ == "__main__": main()