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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