Kolmogorov problem on the class of multiply monotone functions

Necessary and sufficient conditions for positive numbers $M_{k_1}, M_{k_2}, M_{k_3}, M_{k_4}$,$0 = k_1 < k_2<k_2\leq r-2$,$k_4=r$, to guarantee the existence of an $r-1$-monotone function defined on the negative half-line and such that $\mathrm{\parallel }{x}^{(k_i)}\mathrm{\parallel }=M_{k_i}$, $i=1,2,3,4$ were found.