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.
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:
The input limitations for getting 100 points are:
Print n space-separated integers − the result of encrypting the original message.
4 3 2
1 1 1 1
1 1 1
0 1 1 0
3 1 5
1 2 3
4
0 1 2
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.