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 ≤ 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 . 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.

输入描述:

The first line contains two space-separated integers n and k (1 ≤ n ≤ 2000, 0 ≤ k ≤ 109). The next line contains n space-separated integers a1, a2, ..., an — elements of the array a (0 ≤ ai ≤ 109).

输出描述:

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.