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If 109+2(111)(108)+3(112)(107)+⋯+10(119)=109⋅k 10^{9} + 2(11^1)(10^8) + 3(11^2)(10^7) + \cdots+ 10(11^9) = 10^9\cdot k109+2(111)(108)+3(112)(107)+⋯+10(119)=109⋅k, then find the value of kkk.
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