coercing a paramter into an integer in Body Mapping Template, AWS API Gateway - amazon-dynamodb

Question

I've been using a bit of arithmetic in the Body Mapping Template in Integration Request:
#set($now = $context.requestTimeEpoch/1000)
#set($soon = $now + 600)
{
"TableName": "events",
.... [ here get events between $now and $soon]
}
Recently I came to need to pass an offset through a parameter:
#set($now = $context.requestTimeEpoch/1000)
#set($soon = $now + $input.params('offset'))
{
"TableName": "events",
.... [ here get events between $now and $soon] ....
}
It turns out that if $now is 1518939082, with query paramter ?offset=600 $soon will be 1518939082600 - a concatenation. I have tried various ways to force the parameter being recognised as an integer, including:
#set($offset = $Integer.parseInt($input.params('offset')))
#set($offset = 0 + $input.params('offset'))
#set($offset = 1 * $input.params('offset'))
None of them works. I inserted #set($offset = 0) before each test so I can tell "nothing happens" from "a nothingness is returned".
In the first case, $offset prints an empty string, not 0. (This happens to $Integer.parseInt("1") too.)
In the second case, $offset prints a concatenation of "0" and the string value of "offset".
In the third case, $offset prints a 0, as if the entire line doesn't exist.
None of them successfully transformed the parameter to an integer.
Is there a way to use that parameter as an integer?