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>
long long n, k, A[5000], ma[5000], mt[5000], ans[5000] = {0};
void mul_matrix(long long a[5000], long long b[5000], long long c[5000]) {
  long long i, j;
  for (i = 0; i < n; i++)
    for (mt[i] = j = 0; j <= i; j++)
      mt[i] = (mt[i] + a[j] * b[i - j]) % 1000000007L;
  for (i = 0; i < n; i++) c[i] = mt[i];
}
int main() {
  long long i, j, t;
  scanf("%I64d%I64d", &n, &k);
  for (i = 0; i < n; i++) scanf("%I64d", &A[i]);
  for (i = 0; i < n; i++) ma[i] = 1;
  ans[0] = 1;
  while (k) {
    if (k & 1) mul_matrix(ma, ans, ans);
    mul_matrix(ma, ma, ma);
    k >>= 1;
  }
  for (i = 0; i < n; i++) {
    for (t = j = 0; j <= i; j++) t = (t + A[i - j] * ans[j]) % 1000000007L;
    printf("%I64d ", t);
  }
  return 0;
}
