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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.StringTokenizer;

public class PartialSums {
    public static void main(String[] args) {
        InputReader r = new InputReader(System.in);
        int n = r.nextInt();
        int k = r.nextInt();
        long mod = (long) 1e9 + 7;
        long[] arr = new long[n];
        arr[0] = k % mod;
        for (int i = 1; i < n; i++) {
            arr[i] = arr[i - 1] * (k + i);
            arr[i] %= mod;
            arr[i] *= new Integer((BigInteger.valueOf(i +1).modInverse(BigInteger.valueOf(mod))).toString());
            arr[i] %= mod;
        }
//      for(long x:arr)System.out.println(x);
//      System.out.println("--");
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = r.nextLong();
        long[] res = new long[n];
        for (int i = 0; i < res.length; i++) {
            res[i] = a[i] % mod;
            int in=0;
            for (int j = i - 1; j >= 0; j--) {
                res[i] += a[j] * arr[in++];
                res[i] %= mod;
            }
        }
        for (long x : res)
            System.out.print(x+" ");
    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

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

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
                return null;
            }
        }

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

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

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}
