  We study four dimensional N=2 SO/SP supersymmetric gauge theory on R^3\times
S^1 deformed by a tree level superpotential. We will show that the exact
superpotential can be obtained by making use of the Lax matrix of the
corresponding integrable model which is the periodic Toda lattice. The
connection between vacua of SO(2N) and SO(2kN-2k+2) can also be seen in this
framework. Similar analysis can also be applied for SO(2N+1) and SP(2N).
