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D2. Encrypting Messages
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

The Smart Beaver from ABBYY invented a new message encryption method and now wants to check its performance. Checking it manually is long and tiresome, so he decided to ask the ABBYY Cup contestants for help.

A message is a sequence of n integers a1, a2, ..., an. Encryption uses a key which is a sequence of m integers b1, b2, ..., bm (m ≤ n). All numbers from the message and from the key belong to the interval from 0 to c - 1, inclusive, and all the calculations are performed modulo c.

Encryption is performed in n - m + 1 steps. On the first step we add to each number a1, a2, ..., am a corresponding number b1, b2, ..., bm. On the second step we add to each number a2, a3, ..., am + 1 (changed on the previous step) a corresponding number b1, b2, ..., bm. And so on: on step number i we add to each number ai, ai + 1, ..., ai + m - 1 a corresponding number b1, b2, ..., bm. The result of the encryption is the sequence a1, a2, ..., an after n - m + 1 steps.

Help the Beaver to write a program that will encrypt messages in the described manner.

Input

The first input line contains three integers n, m and c, separated by single spaces.

The second input line contains n integers ai (0 ≤ ai < c), separated by single spaces — the original message.

The third input line contains m integers bi (0 ≤ bi < c), separated by single spaces — the encryption key.

The input limitations for getting 30 points are:

  • 1 ≤ m ≤ n ≤ 103
  • 1 ≤ c ≤ 103

The input limitations for getting 100 points are:

  • 1 ≤ m ≤ n ≤ 105
  • 1 ≤ c ≤ 103
Output

Print n space-separated integers — the result of encrypting the original message.

Examples
Input
4 3 2
1 1 1 1
1 1 1
Output
0 1 1 0
Input
3 1 5
1 2 3
4
Output
0 1 2
Note

In the first sample the encryption is performed in two steps: after the first step a = (0, 0, 0, 1) (remember that the calculations are performed modulo 2), after the second step a = (0, 1, 1, 0), and that is the answer.