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
#include <bits/stdc++.h>
using namespace std;
long long int mod = 1000000000 + 7;
int main() {
  long long int n, k, a[2001], i, j;
  cin >> n >> k;
  for (i = 1; i <= n; i++) {
    cin >> a[i];
  }
  long long int c;
  for (i = 1; i <= n; i++) {
    c = 1;
    long long int res = a[i];
    for (j = i - 1; j > 0; j--) {
      c = c * ((i - j + k - 1) % mod) / (i - j);
      c %= mod;
      res += (a[j] * c) % mod;
      res %= mod;
    }
    cout << res << ' ';
  }
  return 0;
}
