[Python] Why does Python's modulus operator (%) not match the Euclidean definition?

Euclidean definition says,

Given two integers a and b, with b ≠ 0, there exist unique integers q and r such that a = bq + r and 0 ≤ r < |b|, where |b| denotes the absolute value of b.
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Based on below observation,

>>> -3 % -2 # Ideally it should be (-2 * 2) + 1
-1
>>> -3 % 2 # this looks fine, (-2 * 2) + 1
1
>>> 2 % -3 # Ideally it should be (-3 * 0) + 2
-1


looks like the % operator is running with different rules.

• link1 was not helpful,
• link2 gives recursive answer, because, as I do not understand how % works, it is difficult to understand How (a // b) * b + (a % b) == a works

My question:

How do I understand the behavior of modulo operator in python? Am not aware of any other language with respect to the working of % operator.

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