Sidewalk Pillars

Many cars are parked on the sidewalk, making it difficult for pedestrians to pass. The city wants to separate parts of the sidewalk from the road by adding small pillars.

The sidewalk is divided into one-meter positions and is written as a string. A dot (.) means that the position is free and could be used for parking. The letter X means that a pillar already occupies that position, so a car cannot use it.

Every car in the city is exactly L meters long. A car can park starting at a position only if there are at least L consecutive free positions from that point.

The city has at most N additional pillars available. It wants to place some of them so that these conditions hold:

1. The number of possible parking starting positions is as small as possible.
2. Among all layouts that satisfy the first condition, use the smallest possible number of additional pillars.

Given N, L, and the current sidewalk layout, output any final layout that satisfies both conditions.

The first line contains two integers N and L (1 <= N, L <= 100): the number of additional pillars available and the length of each car in meters.

The second line contains a string of at most 100 characters describing the current sidewalk. Each character represents one meter. The letter X is a meter already occupied by a pillar, and . is a free meter.

Print the sidewalk layout after adding pillars if needed, using the same format as the input layout.

The correct answer may not be unique.

In the first public test, although three pillars are available, placing two pillars is enough to make parking impossible.

In the second public test, the shown final layout leaves four possible parking starting positions, and no layout can do better.