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 int mod = 1e9 + 7;
const int maxn = 2005;
long long coe[maxn];
int data[maxn];
long long ans[maxn];
int n, k;
long long inv(long long s) {
  int n = mod - 2;
  long long ret = 1;
  for (; n; n >>= 1) {
    if (n & 1) ret = ret * s % mod;
    s = s * s % mod;
  }
  return ret;
}
void init() {
  coe[0] = 1;
  long long now = k;
  for (int i = 1; i <= n + 1; ++i) {
    coe[i] = coe[i - 1] * now++ % mod;
    coe[i] = coe[i] * inv(i) % mod;
  }
}
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; ++i) scanf("%d", data + i);
  if (k == 0) {
    for (int i = 0; i < n; ++i) {
      if (i) putchar(' ');
      printf("%d", data[i]);
    }
    puts("");
    return 0;
  }
  init();
  for (int i = 0; i < n; ++i) {
    for (int j = i, t = 0; j < n; ++j) {
      ans[j] += coe[t++] * data[i] % mod;
    }
  }
  for (int i = 0; i < n; ++i) {
    if (i) putchar(' ');
    printf("%I64d", ans[i] % mod);
  }
  puts("");
  return 0;
}
