Inhabitants of Bytetown love watching sunsets from the roofs of their houses. If a sunset is particularly spectacular, some of them decide to go on the roofs of nearby buildings, so that they have a better view.</p>

Buildings in Bytetown capital are arranged on a grid n × n. Distance between two points is measured using the Manhattan metric.

John plans to buy a new flat. He is a great admirer of sunsets and he is ready to walk to some other building every day to see this inimitable phenomenon. He would not like, however, to walk further than k units away from his flat.

Help John decide where to buy his new flat. For a given plan of the city with heights of all buildings specified, construct a new map, which for each building a specifies the height of the highest building that John can walk to, assuming that he buys a flat in building a.

Write a program which:

• reads from the standard input the plan of the city with heights of all buildings specified,
• for each building calculates the height of the highest building located not further than k units away from it,
• writes the modified map with calculated heights to the standard output.

As a reminder, the Manhattan distance of two points (a_x, a_y) and (b_x, b_y) is ρ((a_x, a_y), (b_x, b_y)) = |a_x - b_x| + |a_y - b_y|.

입력 형식

In the first line of the standard input there are two integers n and k (1 ≤ n ≤ 1500, 1 ≤ k ≤ n), separated by a single space. In each of the following n lines there are n non-negative integers not grater than 1 000 000 000, separated by single spaces - they describe the plan of Bytetown.

출력 형식

In each of n lines of standard output there should be n non-negative integers, separated by single spaces and describing the modified plan of Bytetown.

예제 입력

4 2
1 3 4 5
0 2 2 3
4 1 1 3
6 2 3 0

예제 출력

4 5 5 5
6 4 5 5
6 6 4 5
6 6 6 3