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 <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/cdc22b6f0de971f5a4a64b6f9e22d76a719ec5b7.png" style="max-width: 100.0%;max-height: 100.0%;"/>. The operation *x* *mod* *y* means that we take the remainder of the division of number *x* by number *y*. 1.  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* (*a*<sub class="lower-index">*i*</sub> = *s*<sub class="lower-index">*i*</sub>). 
You task is to find array *a* after exactly *k* described operations are applied.
The first line contains two space-separated integers *n* and *k* (1 ≤ *n* ≤ 2000, 0 ≤ *k* ≤ 10<sup class="upper-index">9</sup>). The next line contains *n* space-separated integers *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub> — elements of the array *a* (0 ≤ *a*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">9</sup>).
n, k = map(int, input().split())
a = list(map(int, input().split()))

m = 1000000007
r = [ 0, 1 ]
for i in range(2, n+1):
    r.append( (- (m // i) * r[m % i]) % m )

c = [ 1 ]
for i in range(1, n):
    c.append((c[i-1] * (k+i-1) * r[i]) % m)

ans = []
for i in range(n):
    t = 0
    for j in range(i+1):
        t = (t + a[j] * c[i-j]) % m
    ans.append(t)

for i in range(n):
    print(ans[i], end=' ')