Long division cryptarithm - KLMN/HIJ = K

The problem statement:

Solve the following long division problem. Each letter represents a unique digit (0-9)

             K
       _______
H I J |K L M N
       O P I Q
      --------
         O K L

Source: Dell Magazine

My attempt to solve it:

I have managed to break the problem down into two equations as shown but I’m not sure if this is how I should be proceeding. There are too many unknowns to be solved with two equations alone. Perhaps there should be an equation that represents the constraint that each variable is unique.

From the division, 2 equations are possible

K x (100H + 10I + J) = (1000 x O) + (100P) + (10I) + (Q)

And

1000 x (K – O) + 100 x (L – P) + 10 x (M – I) + (N – Q) = O x 100 + 10K + L