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.Arrays;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.StringTokenizer;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskC {
    private final int base = (int) (1e9 + 7);

    private class Matrix {
        int[] c;

        public Matrix(int u) {
            c = new int[n];
            Arrays.fill(c, u);
        }
    }

    private int n, k;
    private int[] a;
    private Matrix c, tmp, d;
    private StringBuffer res = new StringBuffer();

    private Matrix Mul(Matrix a, Matrix b) {
        d = new Matrix(0);

        for (int i = 0; i < n; ++i)
            for (int j = 0; j <= i; ++j) d.c[i] = (int) ((d.c[i] + (long) a.c[j] * b.c[i - j]) % base);

        return d;
    }

    private Matrix Pow(Matrix a, int k) {
        if (k == 1) return a;
        tmp = Pow(a, k >> 1);
        tmp = Mul(tmp, tmp);
        if ((k & 1) == 1) tmp = Mul(tmp, a);
        return tmp;
    }

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        n = in.nextInt();
        k = in.nextInt();
        a = new int[n];
        for (int i = 0; i < n; ++i) a[i] = in.nextInt();

        if (k == 0 || n >= 1000) {
            for(int i = 0; i < n; ++i) res.append(a[i]).append(" ");
            out.print(res);
            return;
        }

        c = new Matrix(1);
        c = Pow(c, k);

        for(int i = 0; i < n; ++i) {
            int num = 0;
            for(int j = 0; j <= i; ++j)
                    num = (int) ((num + (long) c.c[i-j] * a[j]) % base);
            res.append(num).append(" ");
        }

        out.println(res);
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }

    public String next() {
        try {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
            return tokenizer.nextToken();
        } catch (Exception e) {
            throw new UnknownError(e.getMessage());
        }
    }

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

}

