3's and 7's

3 and 7 are coprime. For some integer \((x, y)\), the four integer satisfied \[3x+7y=1\] For \(i = 1, 2, 3, \dots\), let \(x_i\) be the sequence of positive integer \(x\) such that \(x_i < x_{i+1}\), each \(x_i\) produce the sequence \(y_i\) of integer \(y\) satisfying the equation above, and \(x_1\) is the least positive integer \(x\)

Find the value of \( \displaystyle \sum_{i=1}^{37}|y_i| \).

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