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 pow(int a, int b, int MOD) {
  long long x = 1, y = a;
  while (b > 0) {
    if (b % 2 == 1) {
      x = (x * y);
      if (x > MOD) x %= MOD;
    }
    y = (y * y);
    if (y > MOD) y %= MOD;
    b /= 2;
  }
  return x;
}
long long InverseEuler(int n, int MOD) { return pow(n, MOD - 2, MOD); }
long long binomialCoeff(int n, int k) {
  if (n < 0) return 1;
  unsigned long long res = 1;
  if (k > n - k) k = n - k;
  for (int i = 0; i < k; ++i) {
    res *= (n - i);
    res %= 1000000007;
    res *= InverseEuler((i + 1), 1000000007);
    res %= 1000000007;
  }
  return res;
}
long long arr[2005];
int N, K;
int main() {
  cin >> N;
  cin >> K;
  for (int i = 0; i < (N); i++) {
    cin >> arr[i];
    if (K == 0) cout << arr[i] << " ";
  }
  if (K == 0) {
    cout << endl;
    return 0;
  }
  vector<long long> Cs;
  for (int i = 0; i < N; i++) {
    Cs.push_back(binomialCoeff(K - 1 + i, i));
    long long res = 0;
    int x = 0;
    for (int j = Cs.size() - 1; j >= 0; j--) {
      res += Cs[j] * arr[x];
      res %= 1000000007;
      x++;
    }
    cout << res << " ";
  }
  cout << endl;
  return 0;
}
