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If DefaultSearchProviderEnabled is on, then setting DefaultSearchProviderSearchURL specifies the URL of the search engine used during a default search. The URL should include the string '{searchTerms}', replaced in the query by the user's search terms.
You can specify Google's search URL as: '{google:baseURL}search?q={searchTerms}&{google:RLZ}{google:originalQueryForSuggestion}{google:assistedQueryStats}{google:searchFieldtrialParameter}{google:searchClient}{google:sourceId}ie={inputEncoding}'.