Henry's constant and solubility According to Henry's law 


  The solubility of gas in a liquid is directly
  proportional to the partial pressure i.e S=Kp


My book says that higher the value of K at a given pressure lower is the solubility of the gas in the liquid. 
I don't understand how. I know I am overseeing something really simple over here as all the books that I have and online websites seem to conclude the same from the given equation. A little help maybe. Thanks.
Actually solubility $x$ is given as a function of pressure $p$ and henry's constant $K_H$:
$$p=K_Hx$$


  My book says that higher the value of K at a given pressure lower is the solubility of the gas in the liquid. I don't understand how.


Since at a given pressure, $p$ is constant, if you increase $K_H$, logically solubility $x$ would decrease.