Given two sets of nonnegative integer numbers:

$X = {x_1, x_2, ... x_n}$ $Y = {y_1, y_2, ... y_m}$

Need to find partition of $X$ on $m$ disjoint subsets, such as sum of elements in $i$-th subset equal to $y_i$.

This generalization of Subset sum problem, which is known to be **NP-Complete**. One of the probable way of solving is to reduce it to system of integer linear equalities. But it's even more general and really hard to solve task. May be one has some fresh ideas?