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 (ai = si).

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

Input

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).

Output

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.

Examples

Input

3 1 1 2 3

Output

1 3 6

Input

5 0 3 14 15 92 6

Output

3 14 15 92 6

inputFormat

Input

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).

outputFormat

Output

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.

Examples

Input

3 1 1 2 3

Output

1 3 6

Input

5 0 3 14 15 92 6

Output

3 14 15 92 6

样例

5 0
3 14 15 92 6

3 14 15 92 6