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.awt.geom.Point2D;
import java.text.*;
import java.math.*;
import java.util.*;

public class Main implements Runnable {

	final String filename = "";

	public void solve() throws Exception {
		int n = iread(), k = iread();
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = iread();

		long[] b = new long[n];
		Arrays.fill(b, 1);
		long[] c = new long[n];
		c[0] = 1;
		while (k > 0) {
			if (k % 2 == 1)
				mul(c, b);
			mul(b, b);
			k /= 2;
		}
		mul(a, c);
		for (int i = 0; i < n; i++) {
			out.write(a[i] + "");
			if (i == n - 1)
				out.write("\n");
			else
				out.write(" ");
		}
	}

	final int mod = 1000000007;

	void mul(long[] a, long[] b) {
		int n = a.length;
		for (int i = n - 1; i >= 0; i--) {
			a[i] = (a[i] * b[0]) % mod;
			for (int j = 0; j < i; j++) {
				a[i] = (a[i] + a[j] * b[i - j]) % mod;
			}
		}
	}

	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new BufferedWriter(new OutputStreamWriter(System.out));
			// in = new BufferedReader(new FileReader(filename+".in"));
			// out = new BufferedWriter(new FileWriter(filename+".out"));
			solve();
			out.flush();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	public int iread() throws Exception {
		return Integer.parseInt(readword());
	}

	public double dread() throws Exception {
		return Double.parseDouble(readword());
	}

	public long lread() throws Exception {
		return Long.parseLong(readword());
	}

	BufferedReader in;

	BufferedWriter out;

	public String readword() throws IOException {
		StringBuilder b = new StringBuilder();
		int c;
		c = in.read();
		while (c >= 0 && c <= ' ')
			c = in.read();
		if (c < 0)
			return "";
		while (c > ' ') {
			b.append((char) c);
			c = in.read();
		}
		return b.toString();
	}

	public static void main(String[] args) {
		try {
			Locale.setDefault(Locale.US);
		} catch (Exception e) {

		}
		// new Thread(new Main()).start();
		new Thread(null, new Main(), "1", 1 << 25).start();
	}
}