3716: Partial Sums
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Description
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 xmody 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 (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