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How does the Spell Sniper work with the sorcerer's Distant Spell?

For my sorcerer character, I chose the "Distant Spell" metamagic option, which allows me to spend sorcery points to extend the range of my spells:

> Distant Spell  
When you Cast a Spell that has a range of 5 feet or greater, you can spend 1 sorcery point to double the range of the spell.  
When you Cast a Spell that has a range of touch, you can spend 1 sorcery point to make the range of the spell 30 feet.

The "[Spell Sniper](http://dnd5e.wikidot.com/feat:spell-sniper)" feat has this description:

> *Prerequisite: The ability to cast at least one spell*
>
> You have learned techniques to enhance your attacks with certain kinds of spells, gaining the following benefits:  
> * When you cast a spell that requires you to make an attack roll, the spell's range is doubled.  
> * Your ranged spell attacks ignore half cover and three-quarters cover.  
> * You learn one cantrip that requires an attack roll. Choose the cantrip from the bard, cleric, druid, sorcerer, warlock, or wizard spell list. Your spellcasting ability for this cantrip depends on the spell list you chose from: Charisma for bard, sorcerer, and warlock; Wisdom for cleric or druid; or Intelligence for wizard.

If I take the Spell Sniper feat, how does this work with Distant Spell? Does the doubled range from the feat apply before or after I use the metamagic? For instance, can I use Distant Spell to imbue a touch attack roll spell, such as Plane Shift or Inflict Wounds, and then cast it from 60 feet away? Or does the doubled range from Spell Sniper apply *before* the metamagic, so that it doubles the range for any ranged spell attack (and so *then* Distant Spell quadruples it) but any touch spell imbued with Distant Spell won't benefit from Spell Sniper?