local p0, q = io.read("*n", "*n") local mat = {} for i = 1, 101 do mat[i] = {} for j = 1, 101 do mat[i][j] = 0 end end local vec = {} --[[ f(p) = p * 1/2 + p * 1/2 * f(p - q) + (1-p) * 1/3 + (1-p) * 1/3 * f(p + q) f(p) - p/2 * f(p-q) - (1-p)/3 * f(p+q) = 1/3 + p/6 ]] for p = 0, 100 do local left = p - q if left < 0 then left = 0 end local right = p + q if 100 < right then right = 100 end local r = p / 100 mat[p + 1][p + 1] = mat[p + 1][p + 1] + 1 mat[p + 1][left + 1] = mat[p + 1][left + 1] + (-r / 2) mat[p + 1][right + 1] = mat[p + 1][right + 1] + (-(1 - r) / 3) vec[p + 1] = 1 / 3 + r / 6 end for i = 1, 101 do local base = mat[i][i] for k = i, 101 do mat[i][k] = mat[i][k] / base end vec[i] = vec[i] / base for j = i + 1, 101 do local mul = mat[j][i] for k = i, 101 do mat[j][k] = mat[j][k] - mul * mat[i][k] end vec[j] = vec[j] - mul * vec[i] end end for i = 101, 1, -1 do for j = i - 1, 1, -1 do vec[j] = vec[j] - mat[j][i] * vec[i] end end print((1 + vec[p0 + 1]) / 3)