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.util.*;
import java.io.*;
public class E {
	final int MOD = (int)Math.pow(10, 9)+7;
	public long factorial(int x, int y){
		long ret = 1;
		int div = 1;
		while( div <= y ){
			ret *= x;
			ret /= div;
			div++;
			x--;
			ret %= MOD;
		}
		return ret;
	}
	public long getNum(int x){
		long temp = MOD+1;
		for(int i = 0;; i += MOD){
			if( temp%x == 0 ){
				break;
			}
			temp += MOD;
		}
		temp /= x;
		return temp%MOD;
	}
	public void solve() throws IOException {
		int n = nextInt();
		int k = nextInt();
		int[] a = new int[n];
		for(int i = 0; i < n; i++){
			a[i] = nextInt();
		}
		long[] coeff = new long[n];
		coeff[0] = 1;
		writer.print(a[0] + " ");
		for(int i = 1; i < n; i++){
			long temp = getNum(i);
			coeff[i] = coeff[i-1]*(k+i-1)%MOD;
			coeff[i] *= temp;
			coeff[i] %= MOD;
			long sum = 0;
			for(int j = i; j >= 0; j--){
				sum += (a[j]*coeff[i-j])%MOD;
				sum %= MOD;
			}
			writer.print(sum%MOD + " ");			
		}
		writer.println();	
		
	}

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

	BufferedReader reader;
	StringTokenizer tokenizer;
	PrintWriter writer;

	public void run() throws IOException {
		try {
			reader = new BufferedReader(new InputStreamReader(System.in));
			tokenizer = null;
			writer = new PrintWriter(System.out);
			solve();
			reader.close();
			writer.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

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

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

	public String nextToken() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			tokenizer = new StringTokenizer(reader.readLine());
		}
		return tokenizer.nextToken();
	}

}
