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;
const double eps(1e-8);
typedef struct mtype {
  long long a[2010];
  void clear() { memset(a, 0, sizeof(a)); }
  void out(int n) {
    for (int i = 0; i < (n - 1); ++i) printf("%I64d ", a[i]);
    printf("%I64d\n", a[n - 1]);
  }
} mtype;
mtype g, x, temp, dtemp;
int n, k;
mtype mul(mtype a, mtype b) {
  dtemp.clear();
  for (int j = 0; j < n; j++)
    for (int k = 0; k <= j; k++) {
      dtemp.a[j] += a.a[k] * b.a[j - k];
      dtemp.a[j] %= 1000000007;
    }
  return dtemp;
}
mtype abmodc(mtype a, int b) {
  temp.clear();
  temp.a[0] = 1;
  while (b) {
    if (b & 1) {
      temp = mul(temp, a);
    }
    a = mul(a, a);
    b >>= 1;
  }
  return temp;
}
int main() {
  scanf("%d %d", &n, &k);
  x.clear();
  for (int i = 0; i < (n); ++i) scanf("%I64d", &x.a[i]);
  for (int i = 0; i < (n); ++i) g.a[i] = 1;
  x = mul(x, abmodc(g, k));
  x.out(n);
}
