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 sumlarge(long long x, long long y) {
  return (((x % 1000000007) + (y % 1000000007)) % 1000000007);
}
long long mutlilarge(long long x, long long y) {
  long long t = x * y;
  long long u = t % 1000000007;
  return u;
}
long long bigmod(long long a, long long p) {
  if (p == 0) return 1;
  long long t = bigmod(a, p / 2);
  t = t * t % 1000000007;
  if (p % 2) t = (t * a) % 1000000007;
  return t;
}
int main() {
  long long n, k;
  long long a[2001], ans[2001];
  scanf("%I64d%I64d", &n, &k);
  for (int i = 1; i <= n; i++) {
    scanf("%I64d", &a[i]);
  }
  ans[1] = a[1];
  for (long long i = 1; i <= n; i++) {
    ans[i] = a[i];
    long long t_head = 1;
    long long t_bot = 1;
    for (long long j = i - 1; j >= 1; j--) {
      long long dif = i - j;
      t_head = mutlilarge(t_head, dif + k - 1);
      t_bot = mutlilarge(t_bot, dif);
      long long t = mutlilarge(t_head, bigmod(t_bot, 1000000005));
      ans[i] = sumlarge(ans[i], mutlilarge(a[j], t));
    }
  }
  for (int i = 1; i <= n; i++) {
    if (i == n) {
      printf("%I64d\n", ans[i]);
    } else {
      printf("%I64d ", ans[i]);
    }
  }
  return 0;
}
