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>
const int MAXN = 2000;
const long long MOD = 1000000007LL;
long long A[MAXN], cn[MAXN];
long long C[MAXN][MAXN];
long long pow_mod(long long a, long long b, long long m) {
  long long ret = 1;
  while (b) {
    if (b & 1) ret = (ret * a) % MOD;
    a = (a * a) % MOD;
    b >>= 1;
  }
  return ret;
}
int main() {
  int n, i, j;
  long long k, a;
  scanf("%d%I64d", &n, &k);
  for (i = 0; i < n; ++i) scanf("%I64d", A + i);
  if (k == 0) {
    for (i = 0; i < n; ++i) printf("%I64d ", A[i]);
    putchar('\n');
    return 0;
  }
  --k;
  cn[0] = 1;
  for (i = 1; i < n; ++i) {
    cn[i] = (cn[i - 1] * (k + i)) % MOD;
    cn[i] = (cn[i] * pow_mod(i, MOD - 2, MOD)) % MOD;
  }
  for (i = 0; i < n; ++i) {
    for (j = 0; j <= i; ++j) C[i][j] = cn[i - j];
    for (; j < n; ++j) C[i][j] = 0;
  }
  for (i = 0; i < n; ++i) {
    for (a = j = 0; j < n; ++j) a = (a + A[j] * C[i][j]) % MOD;
    printf("%I64d ", a);
  }
  putchar('\n');
  return 0;
}
