AT_past202309_i アメ

$ N $ children are standing in line. Initially, the $ i $ -th child from the front has $ A_i $ candies. You are going to repeat the following operation $ M $ times. - Give $ K $ candies to the child with the fewest candies (if there are multiple such children, to the frontmost one among them). Find how many candies the children will have after the $ M $ operations.

The input is given from Standard Input in the following format: > $ N $ $ M $ $ K $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

Let $ B_i $ be the number of candies that the $ i $ -th child from the front will have after the $ M $ operations. Print $ B_1,B_2,\ldots $ , and $ B_N $ in this order, with spaces in between.

### Sample Explanation 1 - The $ 1 $ -st operation gives candies to the $ 3 $ -rd child from the front. Now, the children have $ 3,4,3 $ , and $ 10 $ candies. - The $ 2 $ -nd operation gives candies to the $ 1 $ -st child from the front. Now, the children have $ 5,4,3 $ , and $ 10 $ candies. - The $ 3 $ -rd operation gives candies to the $ 3 $ -rd child from the front. Now, the children have $ 5,4,5 $ , and $ 10 $ candies. ### Constraints - $ 1 \leq N \leq 10^5 $ - $ 1 \leq M \leq 10^{12} $ - $ 1 \leq K \leq 10^5 $ - $ 0 \leq A_i \leq 10^{12} $ - All input values are integers.