Assume a two-level inclusive cache hierarchy, L1 and L2, where L2 is the larger of the two. Consider the following statements:
\[
S_1:\ \text{Read misses in a write-through L1 cache do not result in writebacks of dirty lines to the L2.}
\]
\[
S_2:\ \text{Write allocate policy must be used in conjunction with write-through caches and no-write allocate policy is used with writeback caches.}
\]
Which of the following statements is correct?