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. 
import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		BufferedReader br = new BufferedReader (new InputStreamReader(System.in));
		
		try {
			String[] data = br.readLine().split(" ");
			int n = Integer.parseInt(data[0]);
			int m = Integer.parseInt(data[1]);
			int c = Integer.parseInt(data[2]);
			int[] a = new int[n];
			int[] b = new int[m];
			 
			//reading a sequence
			data = br.readLine().split(" ");
			for(int i = 0; i < n; i++) 
				a[i] = Integer.parseInt(data[i]); 
			
			//reading b sequence
			data = br.readLine().split(" ");
			for(int i = 0; i < m; i++) 
				b[i] = Integer.parseInt(data[i]); 
			
			//calculating
			for(int i = 0; i < n-m +1; i++) {
				for(int j = 0; j < m; j++)
					a[i+j] = (a[i+j]+b[j])%c;
			}
			
			//printing
			for(int i = 0; i < a.length; i++)
				System.out.print(a[i] + " ");
			System.out.println();
		}
		catch(Exception ex) {
			System.out.println("Something went wrong!");
		}

	}

}

