Snuke has decided to play a game, where the player runs a railway company. There are M+1 stations on Snuke Line, numbered 0 through M. A train on Snuke Line stops at station 0 and every d-th station thereafter, where d is a predetermined constant for each train. For example, if d = 3, the train stops at station 0, 3, 6, 9, and so forth.
There are N kinds of souvenirs sold in areas around Snuke Line. The i-th kind of souvenirs can be purchased when the train stops at one of the following stations: stations li, li+1, li+2, ..., ri.
There are M values of d, the interval between two stops, for trains on Snuke Line: 1, 2, 3, ..., M. For each of these M values, find the number of the kinds of souvenirs that can be purchased if one takes a train with that value of d at station 0. Here, assume that it is not allowed to change trains.
The input is given from Standard Input in the following format:
N M l1 r1 : lN rN
Print the answer in M lines. The i-th line should contain the maximum number of the kinds of souvenirs that can be purchased if one takes a train stopping every i-th station.
3 3 1 2 2 3 3 3
3 2 2
7 9 1 7 5 9 5 7 5 9 1 1 6 8 3 4
7 6 6 5 4 5 5 3 2