Divisibility Chains

Define two positive integer sequences {an}\{a_n\} and {bn}\{b_n\} be defined as a1<b1a_1 < b_1, an+1=an+1a_{n+1}=a_n+1 and bn+1=bn+1b_{n+1}=b_n+1. These two sequences form a Divisibility Chain of length nn if aibia_i\mid b_i for i=1ni=1\to n.

The sequences {an}\{a_n\} and {bn}\{b_n\} form the longest possible divisibility chain subject to the restriction that 1<a110001 < a_1\le 1000 and 1<b110001 < b_1 \le 1000. If this divisibility chain has length kk, then find k+ak+bkk+a_k+b_k

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