Problem Description
xk=b*c(2k)+d
F(x)=a0 x0+a1 x1+a2 x2+...+an-1 xn-1
Given n, b, c, d, a0, ..., an-1, calculate F(x0), ..., F(xn-1).
Input
There is only one test case.
First line, four integers, n, b, c, d.
Second line, n integers, a0, ..., an-1.
1<=n<=105
1<= b, c, d <=106
0<=ai<=106
Output
n lines. i-th line contains one integer, F(xi-1).
Since the answers may be very large, you should output them modulo 106+3.
Sample Input
2 1 2 3
0 1
Sample Output
4
7