Beautiful Array
Practice
4.3 (121 votes)
Mathematics
Medium
Problem
84% Success 323 Attempts 30 Points 2s Time Limit 256MB Memory 1024 KB Max Code

Kevin thinks that array A is beautiful if

  • It contains N positive integers.
  • It doesn't contain any bad numbers.
  • There doesn't exist any number x and tuple (y1, y2, ..., yK) such that Ax = Ay1 · Ay2 · ... · AyK (yi < x).

Kevin knows M bad numbers Bi. Kevin also knows that 1 isn't a bad number. Now he wants to find lexicographically smallest beautiful array.

Input format:

The first line of the input contains three numbers N, K, M. The next line contains M integers - Bi.

Output format:

Output N integers - lexicographically smallest beautiful array.

Constraints:

  • 2 ≤ N, K ≤ 2 · 104
  • 0 ≤ M ≤ 2 · 104
  • 0 ≤ Bi ≤ 109
  • N, M, K ≤ 100 in test data worth 20% of all points
  • M = 0 in test data worth 20% of all points

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