solve this problem:

Suppose there are $n$ agents and $m$ items. The value of agent i for item is given by a nonnegative integer $v_{i,j}.$ An agent's value for a set of items is the sum of its values for individual items in that set. The goal is to partition the $m$ items among the $n$ agents in a fair manner.

Denote an allocation by $A$:$=(A_1,A_2,....,A_n),$ where $A_i$ is the subset of items assigned to agent $i.$ We require that for any $ik,A_i{A}_k=$ empty set$($fi$)($i$.$e$.,$ items are not shared between bundles$)$ and

U$i{A}_i$ is the entire set of items $($i$.$e$.,$ no item is left unallocated$).$ An allocation is deemed fair if$,$ for any pair of agents i and $k,$ the value derived by agent i from its bundle $A_i$ is "within an item" of the value it derives from agent $k^{\text{'}}s$ bundle $A_k$; specifically, for every pair of agents i and $k$ and for every item $jin{A}_k,$ we have that Ak$\backslash \{j\},$ where $v_i(S)$ denotes the value of agent i for a subset $S$ of items.

Design a polynomial$-$time algorithm for computing a fair allocation when the agents have dentical valuations, i$.$e$.,$ item $j$ is valued at $v_{j}0$ by every agent $($though$,$ for distinct items jand $j^{\text{'}},$ the values $v_j$ and $v_{j^{\text{'}}}$ may differ$).$