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 xmody 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≤10⁹). The next line contains n space-separated integers a₁,a₂,...,a_n− elements of the array a (0≤a_i≤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.