A Unique 10-digit Number

There exists a unique 10-digit number \(\overline{abcdefghij}\) which contains each of the digits 0, 1, 2, \(\dots\), 9 exactly once, such that for each \(k\), \(1 \le k \le 10\), the number formed by the first \(k\) digits of \(\overline{abcdefghij}\) is divisible by \(k\). For example, for \(k = 4\), the number \(\overline{abcd}\) is divisible by 4.

Find the three-digit number \(\overline{abc}\).

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