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 PartialSums{
    
    public static void main(String[] args){
        Scanner myScanner = new Scanner(System.in);
        int n = myScanner.nextInt();
        int k = myScanner.nextInt();
        long[] data = new long[n];
        for(int i = 0; i < n; i++)
            data[i] = myScanner.nextLong(); 
        long[][] combi = new long[2][n];
        combi[0][0] = 1;
        combi[1][0] = 1;
        for(int i = 1; i < k + 1; i++){
            combi[1][0] = 1;
            for(int j = 1; j < n; j++)
                combi[1][j] = (combi[0][j] + combi[1][j - 1]) % 1000000007;
            for(int j = 0; j < n; j++)
                combi[0][j] = combi[1][j];              
        }
        long[] result = new long[n];
        for(int i = 0; i < n; i++)
            for(int j = 0, m = i; j <= i; j++, m--)
                result[i] += ((data[j] * combi[1][m]) % 1000000009); 
        for(int i = 0; i < n; i++)
            System.out.print(result[i] + " ");
    }
}
