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 ifac[2010], inv[2010], comb[2010];
void predo() {
  inv[1] = ifac[0] = 1;
  for (int i = 2; i < 2010; i++) {
    inv[i] = (inv[1000000007 % i] * (1000000007 - 1000000007 / i)) % 1000000007;
  }
  for (int i = 1; i < 2010; i++) {
    ifac[i] = (ifac[i - 1] * inv[i]) % 1000000007;
  }
}
int main() {
  predo();
  int n, k, a[2010];
  long long ans;
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  if (k == 0) {
    for (int i = 0; i < n; i++) {
      printf("%d ", a[i]);
    }
    puts("");
    return 0;
  }
  comb[0] = 1;
  for (int i = 1; i <= n; i++) {
    comb[i] = ((comb[i - 1] * (k + i - 1)) % 1000000007 * inv[i]) % 1000000007;
  }
  for (int i = 0; i < n; i++) {
    ans = 0;
    for (int j = 0; j <= i; j++) {
      ans = (ans + comb[i - j] * a[j]) % 1000000007;
    }
    printf("%I64d ", ans);
  }
  puts("");
  return 0;
}
