from functools import lru_cache def main(): import sys A, B, C, N = map(int, sys.stdin.readline().split()) @lru_cache(maxsize=None) def dp(k, a, b, c): if k == 0: return (0.0, 0.0, 0.0) total = a + b + c T = total * (total - 1) / 2 if total >= 2 else 0.0 if T <= 1e-9: next_e = dp(k-1, a, b, c) return (next_e[0], next_e[1], next_e[2]) # Calculate possible same-color pairs w_pairs = a * (a - 1) / 2 if a >= 2 else 0.0 b_pairs = b * (b - 1) / 2 if b >= 2 else 0.0 c_pairs = c * (c - 1) / 2 if c >= 2 else 0.0 same_pairs = w_pairs + b_pairs + c_pairs prob_diff = (T - same_pairs) / T # Probabilities prob_w = w_pairs / T prob_b = b_pairs / T prob_c = c_pairs / T # Next states for same-color pairs e_white = dp(k-1, a-1, b, c) if a >= 2 else (0.0, 0.0, 0.0) e_black = dp(k-1, a, b-1, c) if b >= 2 else (0.0, 0.0, 0.0) e_brown = dp(k-1, a, b, c-1) if c >= 2 else (0.0, 0.0, 0.0) # Next state for different pairs e_diff = dp(k-1, a, b, c) # Calculate expected values e_w = prob_w * (1.0 + e_white[0]) + prob_b * e_black[0] + prob_c * e_brown[0] + prob_diff * e_diff[0] e_b = prob_w * e_white[1] + prob_b * (1.0 + e_black[1]) + prob_c * e_brown[1] + prob_diff * e_diff[1] e_c = prob_w * e_white[2] + prob_b * e_black[2] + prob_c * (1.0 + e_brown[2]) + prob_diff * e_diff[2] return (e_w, e_b, e_c) ew, eb, ec = dp(N, A, B, C) print("{0} {1} {2}".format(ew, eb, ec)) if __name__ == '__main__': main()