Dealing with memory caches

How do we deal with a L1 cache that is Write-back Write allocate, and the L2 cache, which is a Write-through Write no-allocate?

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On a cache write miss in the L1 cache, the block is looked for in the L2 cache. If we have a miss at L2 as well, we go to the main memory. However, since the L2 cache was a Write no-allocate, the block is not ...