Problem Description
In the unimaginable popular DotA game, the hero Lich has a wonderful skill: Frost Chain, release a jumping breath of frost that jumps N times against enemy units.
Today iSea play the role of Lich, at first he randomly chooses an enemy hero to release the skill, then the frost jumps for N times. Each time, it make a damage of one HP unit on this hero (including the first time), then bounces to another hero (can’t be himself) if their distance is no more than D and this hero is alive of course, also randomly. Here random means equal probability.
Now we know there are always only five enemy heroes, and also their coordinates and HP value. iSea wonders the death probability of each hero. One hero is dead if its HP is equal to or less than zero.
Input
There are several test cases in the input.
Each test case begin with two integers N and D (1 <= N <= 25, 1 <= D <= 10000).
The following line contains ten integers, indicating the coordinates of the five opponents, and -10000 ≤ x, y ≤ 10000.
Then five integers follows, indicating the HP (1 <= HP <= 5) of five opponents.
The input terminates by end of file marker.
Output
For each test case, output five floating numbers, indicating the death probability of each hero, as the given order, rounded to three fractional digits, and separated by a single blank.
Sample Input
3 100
0 1 0 2 0 3 0 4 0 5
1 1 1 1 1
3 1
0 1 0 2 0 3 0 4 0 5
1 1 1 1 1
Sample Output
0.800 0.800 0.800 0.800 0.800
0.500 0.800 0.800 0.800 0.500
