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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;
import java.util.Stack;

public class ProblemC {
    static long MOD = 1000000007;
    
    static long pow(long a, long x) {
        long res = 1;
        while (x > 0) {
            if (x % 2 != 0) {
                res = (res * a) % MOD;
            }
            a = (a * a) % MOD;
            x /= 2;
        }
        return res;
    }
 
    static long inv(long a) {
        return pow(a, MOD-2) % MOD;
    }
    
    static long comb(long n, long k) {
        long upper = 1;
        for (int nl = 0 ; nl < k ; nl++) {
            upper = (upper * (n - nl)) % MOD;
        }

        long downer = 1;
        for (int nl = 1 ; nl <= k ; nl++) {
            downer = (downer * nl) % MOD;
        }
        return (upper * inv(downer)) % MOD;
    }
    
    public static void main(String[] args) throws IOException {
        BufferedReader s = new BufferedReader(new InputStreamReader(System.in));
        String[] line = s.readLine().split(" ");
        int n = Integer.valueOf(line[0]);
        int k = Integer.valueOf(line[1]);
        
        String[] data = s.readLine().split(" ");
        long[] a = new long[n];
        for (int i = 0 ; i < a.length; i++) {
            a[i] = Long.valueOf(data[i]);
        }
        
        long[] x = new long[n];
        for (int i = 0 ; i < n ; i++) {
            x[i] = comb(i+k-1, i);
        }
        
        StringBuffer ans = new StringBuffer();
        for (int i = 0 ; i < n ; i++) {
            long r = 0;
            for (int j = i ; j >= 0 ; j--) {
                r += x[j] * a[i-j];
                r %= MOD;
            }
            ans.append(r).append(" ");
        }
        System.out.println(ans.substring(0, ans.length()-1));
    }

}