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.*;
import java.math.BigInteger;
import java.util.*;

public class Codeforces {
	FastScanner in;
	PrintWriter out;

	//final long probmod = (long)1e9 + 7;
	final long mod = ((long)1e9 + 7);
	final BigInteger bimod = BigInteger.valueOf(mod);
	
	long inv(long x) {
		if (x % mod == 0) {
			return 0;
		}
		return BigInteger.valueOf(x).modInverse(bimod).longValue();
	}
	
	void solve() {
		int n = in.nextInt();
		long k = in.nextInt();
		long[] a = new long[n];
		for (int i = 0; i < n; i++) {
			a[i] = in.nextInt();
		}
		long[] ainv = new long[n + 1];
		for (int j = 0; j <= n; j++) {
			ainv[j] = inv(j);
		}
		for (int i = 0; i < n; i++) {
			long curc = 1;
			long ans = 0;
			for (int j = 0; j <= i; j++) {
				ans = (ans + a[i - j] * curc) % mod;
				
				if (j != i) {
					curc = (curc * (j + k)) % mod;
					curc = (curc * ainv[j + 1]) % mod;
				}
			}
			out.print(ans + " ");
		}
	}

	void run() {
		in = new FastScanner();
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));

		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {

				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}
	}

	public static void main(String[] args) {
		new Codeforces().run();
	}
}