MY ALGO TIME CONSUMED IS(250+128)*N unit

my method is:

divide distance between [0,32000] to 128 sector
each sector is total of stars that occured in that portion
hence for each x, level x calcute of bottom formula
level = sector[x/250]+ Xpivot[i] that i=int(x/250)*250 to x
in last update value of all sector that indexs greater than this sector index;