Since $a+d$ is odd, there is no carry over from the addition of $b+c$ in the hundreds place. Thus, $b+c<10 \implies b+c=3$ or $5$ or $7$ or $9$. Since $b>c \geq 2$, $(b,c)=(3,2)$, $(5,2)$, $(4,3)$, $(7,2)$, $(6,3)$, $(5,4)$. Since $a \geq 7$, $(a,d)=(7,2)$ or $(8,1)$. If $(b,c)=(3,2)$ or $(5,2)$ or $(7,2)$, then $d=1$, thus $a=8$. Thus, $A$ is $8321$ or $8521$ If $(b,c)=(4,3)$ or $(6,3)$, then $A$ is $8431$ or $8631$ or $7432$ or $8632$. If $(b,c)=(5,4)$, then $A$ is $8541$ or $7542$.