A8745. Partial Sums

You've got an array $a$ , consisting of $n$ integers. The array elements are indexed from 1 to $n$ . Let's determine a two step operation like that:

1. First we build by the array $a$ an array $s$ of partial sums, consisting of $n$ elements. Element number $i$ ( $1<=i<=n$ ) of array $s$ equals . The operation $x mod y$ means that we take the remainder of the division of number $x$ by number $y$ .
2. Then we write the contents of the array $s$ to the array $a$ . Element number $i$ ( $1<=i<=n$ ) of the array $s$ becomes the $i$ -th element of the array $a$ ( $a_{i}=s_{i}$ ).

You task is to find array $a$ after exactly $k$ described operations are applied.

The first line contains two space-separated integers $n$ and $k$ ( $1<=n<=2000$ , $0<=k<=10^{9}$ ). The next line contains $n$ space-separated integers $a_{1},a_{2},...,a_{n}$ — elements of the array $a$ ( $0<=a_{i}<=10^{9}$ ).

Print $n$ integers — elements of the array $a$ after the operations are applied to it. Print the elements in the order of increasing of their indexes in the array $a$ . Separate the printed numbers by spaces.