Resizing / max width image code problem

Sorry, but I’m getting a bit of a problem with this code. While it does indeed resize large images that would otherwise break borders, it also resizes smaller / low res images to the max width too (unless, for some reason, they are captioned). Can anything be added to the code to sort out this issue?

p img {
  width: 100% !important;
  height: auto;
}

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