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, ..., a_n. Encryption uses a key which is a sequence of m integers b₁, b₂, ..., b_m (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, ..., a_m a corresponding number b₁, b₂, ..., b_m. On the second step we add to each number a₂, a₃, ..., a_m + 1 (changed on the previous step) a corresponding number b₁, b₂, ..., b_m. And so on: on step number i we add to each number a_i, a_i + 1, ..., a_{i + m - 1} a corresponding number b₁, b₂, ..., b_m. The result of the encryption is the sequence a₁, a₂, ..., a_n 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 a_i (0 ≤ a_i < c), separated by single spaces — the original message.

The third input line contains m integers b_i (0 ≤ b_i < 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.

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.

Encrypting Messages

Examples