'By all means, take a few.' vs 'At all means, take a few.'

[Harshgupta_04]

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #664 "Prepositional Phrases - At, By, For and To (2)", question 1

You were wondering if you could have a cutting from my jade plant? ......... all means, take a few. You are welcome to take at least three or four.

(a) At
(b) By
(c) For
(d) To

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #664 "Prepositional Phrases - At, By, For and To (2)", answer 1

You were wondering if you could have a cutting from my jade plant? By all means, take a few. You are welcome to take at least three or four.

Correct answer: (b) By

Your answer was: incorrect
You were wondering if you could have a cutting from my jade plant? At all means, take a few. You are welcome to take at least three or four.
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Why not at

[Mister Micawber]

'By all means' is a fixed English phrase. 'At all means' is not.
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Native English teacher at Mister Micawber's