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Efficient solutions to general Bézout’s identity $a_1 b_1 + \dots + a_n b_n = 1$

Suppose I have integers $a_1, \dots, a_n$ which are coprime, meaning that $$a_1 b_1 + \dots + a_n b_n = 1$$ has a solution in integers $b_1, \dots, b_n$. I would like to get a bound saying ...
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