Best quadrature formulas on classes of differentiable periodic functions

A solution is given to the problem of finding the best quadrature formula among formulas of the form
$$ \int_0^{2\pi}f(x)\,dx\approx\sum_{k=0}^{m-1}\sum_{l=0}^\rho p_{k,l}f^{(l)}(x_k) $$
which are exact in the case of a constant, for $\rho=r-1$, $r=1,2,3,\dots$ and $\rho=r-2$, $r$ even, for the classes $W^{(r)}L_qM$ of $2\pi$-periodic functions.