In the six years that passed since the first experimental genie bombardments, Pitirim Schwartz has made considerable advance. His latest invention is an ifrit bottle, which has been developed especially for bombing large cities. Each ifrit from such a bottle ruins everything within a radius of r miles from the impact point. Only a few ifrit bottles are needed to demolish all n large cities of a neighboring country… Alas, Pitirim has very few ifrit bottles, so he has asked programmer Privalov to compute the minimal number of bottles needed for the destruction of all the cities.

For the convenience of aiming, the bottles can only be dropped exactly on cities. The radius of destruction is so large that cities can be regarded as points of the plane. When an ifrit bottle is dropped, any city within or on the border of the destruction zone is demolished.

In the first line you are given integers n and r (1 ≤ n ≤ 30; 1 ≤ r ≤ 1000). The i-th of the following n lines contains the coordinates of the i-th city; these are two integers in the range from 0 to 1000.

In the first line output the minimal number of bottles needed to demolish all the cities. In the following line give the numbers of the cities on which the bottles should be dropped. The numbers must be separated with a space. If there are many ways to drop the bottles you can output any of them.