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 modexpo(long long int base, long long int power) {
  long long int result = 1;
  while (power != 0) {
    if (power & 1) {
      result = (result * base) % 1000000007;
    }
    base = (base * base) % 1000000007;
    power = power >> 1;
  }
  return result;
}
long long int modinverse(long long int num) {
  long long int temp = 1000000007 - 2;
  return modexpo(num, temp);
}
long long int inverse[2010];
void fill() {
  for (long long int i = 0; i < 2010; i++) {
    inverse[i] = modinverse(i);
  }
}
long long int NCK(long long int n, long long int k) {
  long long int ans = 1;
  n = n % 1000000007;
  for (long long int i = 1; i <= k; i++) {
    ans *= (n + 1 - i);
    if (ans >= 1000000007) {
      ans = ans % 1000000007;
    }
    ans = (ans * inverse[i]);
    if (ans >= 1000000007) {
      ans = ans % 1000000007;
    }
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  fill();
  long long int n, k;
  cin >> n >> k;
  long long int arr1[n];
  long long int result[n];
  for (long long int i = 0; i < n; i++) {
    cin >> arr1[i];
    if (k == 0) {
      cout << arr1[i] << " ";
    }
    result[i] = 0;
  }
  if (k == 0) {
    exit(0);
  }
  long long int val1[n];
  for (long long int i = 0; i < n; i++) {
    val1[i] = NCK(k + i - 1, i);
  }
  long long int store;
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 0; j < (n - i); j++) {
      store = val1[j];
      store = (store * arr1[i]);
      if (store >= 1000000007) {
        store = store % 1000000007;
      }
      result[i + j] += store;
      if (result[i + j] >= 1000000007) {
        result[i + j] -= 1000000007;
      }
    }
  }
  for (long long int i = 0; i < n; i++) {
    cout << result[i] << " ";
  }
  return 0;
}
