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.FileNotFoundException;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Locale;
import java.util.Queue;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class Solution implements Runnable {

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st;

	String nextToken() throws Exception {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(in.readLine());
		}
		return st.nextToken();
	}

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

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

	double nextDouble() throws Exception {
		return Double.parseDouble(nextToken());
	}
	
	long modd = 1000000007;
	BigInteger Bmodd = BigInteger.valueOf(modd);
	
	void solve() throws Exception {
		int n = nextInt();
		long k = nextInt() - 1;
		long[] a = new long[n];
		for (int i = 0; i < n; i++) a[i] = nextInt();
		long[] c = new long[n];
		c[0] = 1;
		if (k >= 0) {
			long kk = 0;
			long nn = k;
			for (int i = 1; i < n; i++) {
				c[i] = c[i - 1] * (nn + 1) % modd * BigInteger.valueOf(kk + 1).modInverse(Bmodd).longValue() % modd;
				nn++; kk++;
			}
		}
		long[] ans = new long[n];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j <= i; j++) {
				ans[i] += a[i - j] * c[j];
			}
		}
		for (int i = 0; i < n; i++) {
			out.print(ans[i] + " ");
		}
	}

	public void run() {
		try {
			Locale.setDefault(Locale.UK);
			in = new BufferedReader(new InputStreamReader(System.in));
			// in = new BufferedReader(new FileReader("input.txt"));
			out = new PrintWriter(System.out);
			// out = new PrintWriter("output.txt");
			solve();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		} finally {
			out.close();
		}
	}

	public static void main(String[] args) {
		// new Thread(null, new Solution(), "1", 1 << 28).start();
		(new Solution()).run();
	}

}