A ring of n signal beacons circles a harbor, numbered 0 through n-1 clockwise, with beacon n-1 followed again by beacon 0. Each beacon i currently broadcasts a raw strength code[i]. A single calibration key k recalculates every beacon's displayed strength at once, using only the original raw strengths (never the newly recalculated ones):

• If k > 0, beacon i's new strength becomes the sum of the raw strengths of the k beacons immediately clockwise of it (the next k beacons, wrapping around the ring as needed).
• If k < 0, beacon i's new strength becomes the sum of the raw strengths of the |k| beacons immediately counter-clockwise of it (the previous |k| beacons, wrapping around the ring as needed).
• If k = 0, every beacon's new strength becomes 0.

Compute the new strength of every beacon.

Input format

Line 1: two integers n and k. Line 2: n integers code[0] ... code[n-1], the raw strengths.

Output format

Print n space-separated integers: the recalculated strengths, in beacon order 0..n-1.

Constraints

• 1 <= n <= 100
• 1 <= code[i] <= 100
• -(n // 2) <= k <= n // 2 (integer division)

6 2
2 4 6 8 10 12

10 14 18 22 14 6

4 -2
3 5 2 7

9 10 8 7