CF354C Vasya and Beautiful Arrays

Vasya's got a birthday coming up and his mom decided to give him an array of positive integers $ a $ of length $ n $ . Vasya thinks that an array's beauty is the greatest common divisor of all its elements. His mom, of course, wants to give him as beautiful an array as possible (with largest possible beauty). Unfortunately, the shop has only one array $ a $ left. On the plus side, the seller said that he could decrease some numbers in the array (no more than by $ k $ for each number). The seller can obtain array $ b $ from array $ a $ if the following conditions hold: $ b_{i}>0; 0

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In the first sample we can obtain the array: $ 3 6 9 12 12 15 $ In the second sample we can obtain the next array: $ 7 21 49 14 77 $