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 mod = 1000ll * 1000ll * 1000ll + 7;
long long c[2100];
long long inv[2100];
long long num[2100];
int n, k;
void init() {
  inv[0] = inv[1] = 1;
  for (int i = 2; i <= n; ++i) {
    inv[i] = (-mod / i * inv[mod % i] % mod + mod) % mod;
  }
}
long long getc(int n, int m) {
  long long ans = 1;
  for (int i = 1; i <= m; ++i) ans = (ans * inv[i]) % mod * (n - i + 1) % mod;
  return ans;
}
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; ++i) scanf("%I64d", &num[i]);
  if (k == 0) {
    for (int i = 0; i < n; ++i) printf("%I64d ", num[i]);
    puts("");
  } else {
    init();
    for (int i = 0; i < n; ++i) {
      c[i] = getc(i + k - 1, i);
    }
    long long ans;
    for (int i = 0; i < n; ++i) {
      ans = 0;
      for (int j = 0; j <= i; ++j) ans = (ans + num[j] * c[i - j]) % mod;
      printf("%I64d ", ans);
    }
    puts("");
  }
  return 0;
}
