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 \le 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 \le ai \lt c), separated by single spaces - the original message.

The third input line contains m integers bi (0 \le bi \lt c), separated by single spaces - the encryption key.

The input limitations for getting 30 points are:
1 \le m \le n \le 103 1 \le c \le 103
The input limitations for getting 100 points are:
1 \le m \le n \le 105 1 \le c \le 103

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

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.