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 long long MOD = 1000000007;
long long a[10000], s[10000];
long long m[2010], c[2010];
int n;
long long k;
void ready1() {
  int tmpk = (int)k;
  m[0] = 1;
  m[1] = 1;
  for (int i = 2; i < 2002; i++)
    m[i] = (((-MOD / i) % MOD + MOD) * m[MOD % i]) % MOD;
}
void ready2() {
  c[0] = 1ll;
  for (int i = 1; i < n; i++) c[i] = c[i - 1] * (k + i - 1) % MOD * m[i] % MOD;
}
int main() {
  ready1();
  while (scanf("%d%I64d", &n, &k) != EOF) {
    for (int i = 0; i < n; i++) scanf("%I64d", &a[i]);
    if (!k) {
      for (int i = 0; i < n; i++)
        if (!i)
          printf("%I64d", a[i]);
        else
          printf(" %I64d", a[i]);
      printf("\n");
    } else {
      ready2();
      for (int i = 0; i < n; i++) {
        s[i] = 0;
        for (int j = i; j >= 0; j--)
          s[i] = (s[i] + c[(i - j)] * a[j] % MOD) % MOD;
      }
      for (int i = 0; i < n; i++) printf("%I64d ", s[i]);
      printf("\n");
    }
  }
  return 0;
}
