Bloody Mary Deviled Eggs

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12 large hard-boiled eggs

1/4 cup mayonnaise 

2 tablespoons cocktail sauce 

1 tablespoon tomato paste 

1 tablespoon prepared horseradish 

2 tablespoons paprika 

2 teaspoons hot sauce, such as Tabasco

Juice of 1/2 lemon 

Seafood seasoning, such as Old Bay, for serving

Thinly sliced olives with pimentos, for garnish 

Celery, cut into matchsticks, plus celery leaves, for serving