There are $40$ identical gas cylinders, gas pressure values in which we are unknown and may be evil. It is allowed to connect any cylinders with each other in an amount not exceeding a given natural number $k$, and then separate them; while the pressure gas in the connected cylinders is set equal to the arithmetic average of the pressures in them before the connection. At what minimum $k$ is there a way to equalize the pressures in all $40$ cylinders, regardless of initial pressure distribution in the cylinders?