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 <image>. 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
import java.util.*;

public class c
{
	final int mod = 1000*1000*1000+7;
	final int l = 30;
	private void multiply(int[] a, int[] b, int[] res)
	{
		int n = a.length;
		int[] tmp = new int[n];
		for(int i = 0; i < n; i++)
		{
			tmp[i] = 0;
			for(int j = 0; j <= i; j++)
			{
				tmp[i] += (long)a[j]*b[i-j]%mod;
				tmp[i] %= mod;
			}
		}
		for(int i = 0; i < n; i++)
			res[i] = tmp[i];
	}
	private void run()
	{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		int[][] a = new int[l][n];
		for(int i = 0; i < n; i++)
			a[0][i] = 1;
		for(int i = 1; i < l; i++)
			multiply(a[i-1], a[i-1], a[i]);
		int[] res = new int[n];
		for(int i = 0; i < n; i++)
			res[i] = sc.nextInt();
		for(int i = 0; (1<<i) <= k; i++)
			if((k&(1<<i)) != 0)
				multiply(res, a[i], res);
		for(int i = 0; i < n; i++)
			System.out.format("%d ", res[i]);
	}
	public static void main(String[] args) { new c().run(); }
}
