Problem:
Score : 1400 points

Problem Statement

Snuke got an integer sequence from his mother, as a birthday present. The sequence has N elements, and the i-th of them is i.
Snuke performs the following Q operations on this sequence. The i-th operation, described by a parameter q_i, is as follows:

Take the first q_i elements from the sequence obtained by concatenating infinitely many copy of the current sequence, then replace the current sequence with those q_i elements.

After these Q operations, find how many times each of the integers 1 through N appears in the final sequence.

Constraints

1 ≦ N ≦ 10^5

0 ≦ Q ≦ 10^5

1 ≦ q_i ≦ 10^{18}

All input values are integers.

Input

The input is given from Standard Input in the following format:

N Q
q_1
:
q_Q

Output

Print N lines. The i-th line (1 ≦ i ≦ N) should contain the number of times integer i appears in the final sequence after the Q operations.

Sample Input 1

5 3
6
4
11

Sample Output 1

3
3
3
2
0

After the first operation, the sequence becomes: 1,2,3,4,5,1.

After the second operation, the sequence becomes: 1,2,3,4.

After the third operation, the sequence becomes: 1,2,3,4,1,2,3,4,1,2,3.

In this sequence, integers 1,2,3,4,5 appear 3,3,3,2,0 times, respectively.

Sample Input 2

10 10
9
13
18
8
10
10
9
19
22
27

Sample Output 2

7
4
4
3
3
2
2
2
0
0

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Data.List (foldl', unfoldr)
import Data.Maybe (fromJust)

main :: IO ()
main = mapM_ print . solve . map read . words =<< getContents

solve :: [Int] -> [Int]
solve (n:_:qs) = let ps = concatMap (uncurry (flip replicate)) $ foldl' f [(n, 1)] qs'
                     in [ length $ filter (>=k) ps | k <- [1..n] ]
  where f [(n', _)] x = fst $ fromJust $ g (x, [(n', x)])
        f xs x = concat $ unfoldr g (x, cycle xs)
        g (a, ((b, c) : ys))
          | a == 0 = Nothing
          | b * c <= a = Just ([(b, c)], (a - b * c, ys))
          | otherwise = Just (filter ((>0).fst) [(b, d), (m, 1)], (0, ys))
          where (d, m) = a `divMod` b
        qs' = let q = minimum qs in q : reverse (takeWhile (/=q) (reverse qs))