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:
First we build by the array a an array s of partial sums, consisting of n elements. Element number i (1 \le i \le n) of array s equals . The operation xmody means that we take the remainder of the division of number x by number y. Then we write the contents of the array s to the array a. Element number i (1 \le i \le n) of the array s becomes the i-th element of the array a (ai=si).
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 \le n \le 2000, 0 \le k \le 109). The next line contains n space-separated integers a1,a2,...,an- elements of the array a (0 \le ai \le 109).

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.