When finding the maximum margin separator in the primal form we have the quadratic program

$$min\frac{1}{2}||\theta||^2$$ $$\text{ subject to: } y^{(t)}(\theta \cdot x^{(t)} + \theta_0) \geq 1, \ t=1,...,n,$$

saying basically to find the maximum margin separator. The margin size will be:

$$\frac{1}{||\theta||}.$$

Does the size of the margin change if we change the constants of the constraint?

That is, if we have

$$\text{ subject to: } y^{(t)}(\theta \cdot x^{(t)} + \theta_0) \geq k, \ t=1,...,n,$$

instead of 1?

If it does not matter, why doesn't this matter? How is it an equivalent formulation regardless of the exact constants for the constraint?