A search engine uses an index to retrieve documents for a query. At the very least, an index consists of a set of inverted lists $($one for each vocabulary term$),$ and each inverted list contains the list of document IDs where the term appears $($example below$).$

$$

jack

and

$...$

jill

df$=120$

df$=10122$

$...$

df$=543$

$1$

$34$

$...$

$5$

$34$

$325$

$...$

$56$

$54$

$641$

$...$

$789$

$565$

$864$

$...$

$897$

$....$

$...$

$...$

$...$

$$

$$

$$

$$

Why are the inverted lists sorted in ascending order of document ID$?$

Please explain how this is useful during Boolean retrieval.