Reactor Core Rebalancing

A fusion test facility has n reactor cores arranged in a line, each with an initial power rating. An automated rebalancing routine runs for exactly k cycles. In every cycle, the routine finds the core with the currently lowest power rating -- choosing the leftmost such core if several cores are tied for lowest -- and multiplies that core's power rating by a fixed booster factor, permanently increasing it.

After all k cycles have run, report the final power rating of every core, in their original left-to-right order.

Input format

Line 1: three integers n, k, and multiplier. Line 2: n integers, the initial power ratings, in core order.

Output format

A single line with n space-separated integers: the final power rating of each core, in original order.

Constraints

• 1 <= n <= 100
• 1 <= k <= 10
• 1 <= multiplier <= 5
• 1 <= power rating <= 100 for every core, initially

4 3 2
2 5 6 3

8 5 6 6

3 2 3
1 1 1

3 3 1