2. Given 99 | $\overline{62 x y 427}$. Find $950 x+24 y+1$. (1997, Hope Cup Mathematics Invitational)

Find the value of $950 x+24 y+1$ if 99 divides $\overline{62 x y 427}$. (1997, Hope Cup Mathematics Invitational)
(提示: From $91 \overline{62 x y 427}$, we get $91(x+y+21)$. Therefore, $9 \mid(x+y+3)$. Noting that $3 \leqslant x+y+3 \leqslant$ 21, hence $x+y=6$ or 15. From $11 \overline{62 x y 427}$, we get $x-$ $y=-2$ or 9. Also note that $x+y$ and $x-y$ have the same parity, solving gives $(x, y)=(2,4)$. Therefore, $950 x+24 y+1=$ 1997.)