Concat Palindrome

Chef has two strings $A$ and $B$ of lengths $N$ and $M$ respectively. Chef can rearrange both strings in any way he wants. Let the rearranged string of $A$ be $A'$ and the rearranged string of $B$ be $B'$. Determine whether we can construct rearrangements $A'$ and $B'$ such that $(A' + B')$ is a palindrome. Here $+$ denotes the concatenation operation. For e.g. ${abc} + {xyz} = {abcxyz}$. Not