Vision has finally made it to Wakanda to get his MindStone extracted. The MindStone was linked to his brain in a highly sophisticated manner and Shuri had to solve a complex problem to extract the stone. The MindStone had $n$ integers inscribed in it and Shuri needs to apply the prefix sum operation on the array $k$ times to extract the stone.
Formally, given $n$ integers $A[1], A[2] ..... A[n]$ and a number $k$, apply the operation
$A[i] = \sum_{j=1}^{i} A[j]$
on the array $k$ times.
Finally Shuri needs to apply $modulo$ $(10^9 + 7)$ operation to each element of the array. Can you help Shuri accomplish this task before Thanos gets to them?

-----Input:-----
- First line of the input consists of two space separated integers $n$ and $k$. 
- Second line contains $n$ space separated integers $A[1] .. A[n]$.

-----Output:-----
In a single line print $n$ space separated integers, the values of the resultant array after applying all the operations.

-----Constraints-----
- $1 \leq n \leq 1000$
- $1 \leq k \leq 10^{12}$
- $1 \leq A[i] \leq 10^9$

-----Subtasks-----
- 20 Points: $1 \leq k \leq 1000$
- 30 Points: $1 \leq k \leq 1000000$
- 50 Points: Original Constraints

-----Sample Input:-----
$4$ $2$
$3$ $4$ $1$ $5$

-----Sample Output:-----
$3$ $10$ $18$ $31$

-----EXPLANATION:-----
After applying the prefix sum operation once the array becomes -> $3$ $7$ $8$ $13$
After applying the prefix sum operation for the second time, the array becomes -> $3$ $10$ $18$ $31$
After applying $modulo$ $(10^9 +7)$ operation, array becomes -> $3$ $10$ $18$ $31$

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'm=list(map(int,input().strip().split()))[:2]\r\nn,k=m\r\nlst=list(map(int,input().strip().split()))[:n]\r\n\r\nh=0\r\nwhile k!=0:\r\n    sum=0\r\n    for i in range(n):\r\n        i=i+h\r\n\r\n        sum+=lst[i]\r\n        lst.append(sum)\r\n    k-=1\r\n    h+=n\r\nM = 1000000007\r\n# print(lst)\r\nfor j in range (len(lst)-n,len(lst)):\r\n    \r\n    print(lst[j]%M,end=" ")\r\n    '
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13307