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;
int a[2010];
int invs[2010];
int mod = 1000000007;
int r(int a, int s) {
  if (s == 0) return 1;
  long long k = r(a, s / 2);
  k *= k;
  k %= mod;
  if (s & 1) {
    k *= a;
    k %= mod;
  }
  return k;
}
int main() {
  int n, k;
  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) {
      if (i) printf(" ");
      printf("%d", a[i]);
    }
    printf("\n");
    return 0;
  }
  for (int i = (1); i < (n + 1); ++i) invs[i] = r(i, mod - 2);
  for (int i = (0); i < (n); ++i) {
    int res = a[i];
    int curn = k - 1;
    int curm = 0;
    long long curc = 1;
    for (int j = i - 1; j >= 0; --j) {
      curn++;
      curm++;
      curc *= curn;
      curc %= mod;
      int inv = invs[curm];
      curc *= inv;
      curc %= mod;
      long long k = curc * a[j];
      k %= mod;
      res += k;
      if (res >= mod) res -= mod;
    }
    if (i) printf(" ");
    printf("%d", res);
  }
  printf("\n");
  return 0;
}
