223_C. Partial Sums
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
```python
n, k = map(int, input().split())
num = list(map(int, input().split()))
MOD = 10 ** 9 + 7

cf = [1]
for i in range(1, 2020):
    cf.append((cf[-1] * (k + i - 1) * pow(i, MOD - 2, MOD)) % MOD)

ans = [0 for i in range(n)]
for i in range(n):
    for j in range(i + 1):
        ans[i] = (ans[i] + cf[i - j] * num[j]) % MOD

print(' '.join(map(str, ans)))




# Made By Mostafa_Khaled
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