local mfl, mce = math.floor, math.ceil local function encode(a, b, c) return a + (b - 1) * 50 + (c - 1) * 2500 end local function decode(idx) local c = mce(idx / 2500) idx = idx - (c - 1) * 2500 local b = mce(idx / 50) local a = idx - (b - 1) * 50 return a, b, c end local tot = encode(50, 50, 50) local fa, fb, fc, n = io.read("*n", "*n", "*n", "*n") local dp1, dp2 = {}, {} for i = 1, tot do dp1[i] = 0 end dp1[encode(fa, fb, fc)] = 1 for i = 1, n do local src = i % 2 == 1 and dp1 or dp2 local dst = i % 2 == 1 and dp2 or dp1 for j = 1, tot do dst[j] = 0 end for j = 1, tot do local a, b, c = decode(j) local rate = 0 local sum = a + b + c if 1 < a then local z = a * (a - 1) / sum / (sum - 1) rate = rate + z local d = encode(a - 1, b, c) dst[d] = dst[d] + src[j] * z end if 1 < b then local z = b * (b - 1) / sum / (sum - 1) rate = rate + z local d = encode(a, b - 1, c) dst[d] = dst[d] + src[j] * z end if 1 < c then local z = c * (c - 1) / sum / (sum - 1) rate = rate + z local d = encode(a, b, c - 1) dst[d] = dst[d] + src[j] * z end dst[j] = dst[j] + src[j] * (1 - rate) end end local aa, ab, ac = 0, 0, 0 local tbl = n % 2 == 1 and dp2 or dp1 for i = 1, tot do local a, b, c = decode(i) aa = aa + (fa - a) * tbl[i] ab = ab + (fb - b) * tbl[i] ac = ac + (fc - c) * tbl[i] end print(aa .. " " .. ab .. " " .. ac)