Little Bolek has found a picture with n mountain peaks painted on it. The n painted peaks are represented by a non-closed polyline, consisting of 2 n segments. The segments go through 2 n + 1 points with coordinates (1, y 1 ) , (2, y 2 ) , ... , (2 n + 1, y 2 n + 1 ) , with the i -th segment connecting the point ( i , y i ) and the point ( i + 1, y i + 1 ) . For any even i (2 ≤ i ≤ 2 n ) the following condition holds: y i - 1 < y i and y i > y i + 1 . We shall call a vertex of a polyline with an even x coordinate a mountain peak . Bolek fancied a little mischief. He chose exactly k mountain peaks, rubbed out the segments that went through those peaks and increased each peak's height by one (that is, he increased the y coordinate of the corresponding points). Then he painted the missing segments to get a new picture of mountain peaks. Let us denote the points through which the new polyline passes on Bolek's new picture as (1, r 1 ) , (2, r 2 ) , ... , (2 n + 1, r 2 n + 1 ) . Given Bolek's final picture, restore the initial one. The first line contains two space-separated integers n and k (1 ≤ k ≤ n ≤ 100) . The next line contains 2 n + 1 space-separated integers r 1 , r 2 , ..., r 2 n + 1 (0 ≤ r i ≤ 100) — the y coordinates of the polyline vertices on Bolek's picture. It is guaranteed that we can obtain the given picture after performing the described actions on some picture of mountain peaks. Print 2 n + 1 integers y 1 , y 2 , ..., y 2 n + 1 — the y coordinates of the vertices of the polyline on the initial picture. If there are multiple answers, output any one of them.