The Smart Beaver from ABBYY began to develop a new educational game for children. The rules of the game are fairly simple and are described below.

The playing field is a sequence of n non-negative integers ai numbered from 1 to n. The goal of the game is to make numbers a1, a2, ..., ak (i.e. some prefix of the sequence) equal to zero for some fixed k (k < n), and this should be done in the smallest possible number of moves.

One move is choosing an integer i (1 ≤ i ≤ n) such that ai > 0 and an integer t (t ≥ 0) such that i + 2t ≤ n. After the values of i and t have been selected, the value of ai is decreased by 1, and the value of ai + 2t is increased by 1. For example, let n = 4 and a = (1, 0, 1, 2), then it is possible to make move i = 3, t = 0 and get a = (1, 0, 0, 3) or to make move i = 1, t = 1 and get a = (0, 0, 2, 2) (the only possible other move is i = 1, t = 0).

You are given n and the initial sequence ai. The task is to calculate the minimum number of moves needed to make the first k elements of the original sequence equal to zero for each possible k (1 ≤ k < n).

Input

The first input line contains a single integer n. The second line contains n integers ai (0 ≤ ai ≤ 104), separated by single spaces.

The input limitations for getting 20 points are: 

  * 1 ≤ n ≤ 300



The input limitations for getting 50 points are: 

  * 1 ≤ n ≤ 2000



The input limitations for getting 100 points are: 

  * 1 ≤ n ≤ 105

Output

Print exactly n - 1 lines: the k-th output line must contain the minimum number of moves needed to make the first k elements of the original sequence ai equal to zero.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams, or the %I64d specifier.

Examples

Input

4
1 0 1 2


Output

1
1
3


Input

8
1 2 3 4 5 6 7 8


Output

1
3
6
10
16
24
40
import sys
from sys import stdin , stdout

def getInput() :
    sys.stdin.readline()
    return [ int( x ) for x in sys.stdin.readline().split() ]

def setOutput( ns ) :
    for el in ns :
        sys.stdout.write( str( el ) + '\n')

def jumps( maxim , minim ) :
    jump = 1 ;
    while ( jump < minim ) :
        jump *= 2
    if ( jump > maxim ) :
        jump /= 2
    res = 1
    while ( minim > jump ) :
        maxim -= jump
        minim -= jump
        while ( jump > maxim ) :
            jump /= 2
        res += 1
    return res


def solve1( inp ) :
    res = []
    total = 0
    for k in range( 1 , len( inp ) ) :
        total = 0
        for i in range( k ) :
            total += inp[ i ] * jumps( ( len( inp ) - i - 1 ) , ( k - i ) )
        res.append( total )
    return res

def degree2( x ) :
    res = 1
    while( res <= x ) :
        res *= 2
    return res / 2

def solve2( inp ) :
    le = len( inp )
    res = [ 0 for x in range( le - 1 ) ]
    add = 0
    for k in range( le - 1 ) :
        jump = degree2( le - k - 1 )
        add += inp[ k ]
        res[ k ] += add
        inp[ k + jump ] += inp[ k ]
    return res





def main():
    setOutput( solve2( getInput() ) )

if __name__ == '__main__':
    main()
