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.util.*;
import java.lang.reflect.Array;
import java.math.*;

public class C implements Runnable {
	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer st;
	static Random rnd;

	final static long MODULO = 1000000007;

	void solve() throws IOException {
		int n = nextInt(), k = nextInt();

		long[] topFactorials = new long[n];

		topFactorials[0] = 1;

		for (int i = 1; i < n; i++) {
			long mod = (k + i - 1) % MODULO;
			topFactorials[i] = (topFactorials[i - 1] * mod) % MODULO;
		}

		long[] bottomFactorials = new long[n];

		bottomFactorials[0] = 1;

		for (int i = 1; i < n; i++) {
			bottomFactorials[i] = (bottomFactorials[i - 1] * i) % MODULO;
		}

		long[] c = new long[n];

		for (int i = 0; i < n; i++) {
			long a = topFactorials[i], b = BigInteger
					.valueOf(bottomFactorials[i])
					.modInverse(BigInteger.valueOf(MODULO)).longValue()
					% MODULO;

			c[i] = (a * b) % MODULO;
		}

		long[] a = new long[n];

		for (int i = 0; i < n; i++)
			a[i] = nextLong();

		long[] res = new long[n];

		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				long curC = (i - j >= 0) ? c[i - j] : 0;

				res[i] += curC * a[j];
				res[i] %= MODULO;

				if (res[i] < 0)
					res[i] += MODULO;
			}
		}

		for (int i = 0; i < n; i++) {
			out.print(res[i]);
			out.print((i + 1) == n ? "\n" : " ");
		}
	}

	public static void main(String[] args) {
		// final boolean oldChecker = false;
		//
		// if (oldChecker)
		// new Thread(null, new Template(), "yarrr", 1 << 24).start();
		// else
		new C().run();
	}

	public void run() {
		try {
			// final String className = this.getClass().getName().toLowerCase();
			//
			// try {
			// in = new BufferedReader(new FileReader(className + ".in"));
			// out = new PrintWriter(new FileWriter(className + ".out"));
			// } catch (FileNotFoundException e) {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			// }

			rnd = new Random();

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(42);
		}
	}

	String nextToken() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String line = in.readLine();

			if (line == null)
				return null;

			st = new StringTokenizer(line);
		}

		return st.nextToken();
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}