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 power(long long int b, long long int e, long long int m) {
  assert(e >= 0);
  long long int ans = 1;
  b %= m;
  if (b == 0) return 0;
  while (e) {
    if (e & 1) ans = (ans * b) % m;
    e >>= 1;
    b = (b * b) % m;
  }
  return ans;
}
long long int inv(long long int x) {
  return power(x, 1000000007 - 2, 1000000007);
}
void swagWaalaFunction() {
  long long int n, k;
  cin >> n >> k;
  vector<long long int> v(n + 1), coef(n + 1, 1);
  for (int i = 1; i <= n; i++) cin >> v[i];
  long long int prod = 1;
  for (long long int i = 1; i <= n; i++) {
    prod = (prod * (k + i - 1)) % 1000000007;
    prod = (prod * inv(i)) % 1000000007;
    coef[i] = prod;
  };
  for (int i = 1; i <= n; i++) {
    long long int ans = 0, c = 0;
    for (int j = i; j >= 1; j--) {
      ans = (ans + coef[c] * v[j]) % 1000000007;
      c++;
    }
    cout << ans << " ";
  }
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int tc = 1;
  for (int i = 0; i < tc; i++) {
    swagWaalaFunction();
  }
  return 0;
}
