You've got a non-decreasing sequence x 1 , x 2 , ..., x n (1 ≤ x 1 ≤ x 2 ≤ ... ≤ x n ≤ q ) . You've also got two integers a and b ( a ≤ b ; a ·( n - 1) < q ) . Your task is to transform sequence x 1 , x 2 , ..., x n into some sequence y 1 , y 2 , ..., y n (1 ≤ y i ≤ q ; a ≤ y i + 1 - y i ≤ b ) . The transformation price is the following sum: . Your task is to choose such sequence y that minimizes the described transformation price. The first line contains four integers n , q , a , b (2 ≤ n ≤ 6000; 1 ≤ q , a , b ≤ 10 9 ; a ·( n - 1) < q ; a ≤ b ) . The second line contains a non-decreasing integer sequence x 1 , x 2 , ..., x n (1 ≤ x 1 ≤ x 2 ≤ ... ≤ x n ≤ q ) . In the first line print n real numbers — the sought sequence y 1 , y 2 , ..., y n (1 ≤ y i ≤ q ; a ≤ y i + 1 - y i ≤ b ) . In the second line print the minimum transformation price, that is, . If there are multiple optimal answers you can print any of them. The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6 .