Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
C. Partial Sums

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou'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:

- 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 . The operation*x**mod**y*means that we take the remainder of the division of number*x*by number*y*. - 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*_{i}=*s*_{i}).

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* ≤ 10^{9}). The next line contains *n* space-separated integers *a*_{1}, *a*_{2}, ..., *a*_{n} — elements of the array *a* (0 ≤ *a*_{i} ≤ 10^{9}).

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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/11/2021 13:23:53 (i1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|