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{
    
    private final static int MODULO = (int)(1e9 + 7);
    
    private static int[] mulMatrix(int[] a, int[] b){
        int[] result = new int[a.length];
        for(int i = 0; i < a.length; i++){
            long r = 0;
            for(int j = 0; j <= i ; j++)
                r += ( (a[j] * (long) b[i - j]) % MODULO);
            r %= MODULO;    
            result[i] = (int) r;
        }
        return result; 
    }
    
    private static int[] expoFast(int[] a, int k){
        if( k == 0){    
            int[] result = new int[a.length];
            result[0] = 1;
            return result;
        }else if( k % 2 == 0)
            return expoFast(mulMatrix(a, a), k / 2);
        else
            return mulMatrix(a, expoFast(a, k - 1));    
    }   

    public static void main(String[] args){
        Scanner myScanner = new Scanner(System.in);
        int n = myScanner.nextInt();
        int k = myScanner.nextInt();
        int[] data = new int[n];
        for(int i = 0; i < n; i++) data[i] = myScanner.nextInt();
        int[] result = new int[n];
        Arrays.fill(result, 1);
        result = expoFast(result, k);
        result = mulMatrix(result, data);
        for(int i = 0; i < n; i++)
            System.out.print(result[i] + " ");
    }
}
