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.File;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;


public class D {

	public static void main(String[] args) throws IOException {
		solve();
	}
	
	
	private static void solve() throws  IOException {
		BufferedReader in;
		PrintWriter out;
		try {
			in = new BufferedReader(new FileReader("in.txt"));
			out = new PrintWriter(new File("out.txt"));
		} catch (Exception e) {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(new OutputStreamWriter(System.out));
		}
		 
		StringTokenizer tok = new StringTokenizer(in.readLine());
		int n = Integer.valueOf(tok.nextToken());
		int m = Integer.valueOf(tok.nextToken());
		int c = Integer.valueOf(tok.nextToken());
		
		int[] a = new int[n];
		int[] b = new int[m];
		
		tok = new StringTokenizer(in.readLine());
		for (int i = 0; i < n; i++) {
			a[i] = Integer.valueOf(tok.nextToken());
		}
		
		tok = new StringTokenizer(in.readLine());
		for (int i = 0; i < m; i++) {
			b[i] = Integer.valueOf(tok.nextToken());
		}
		for (int i = 0; i <= n-m; i++) {
			for (int j = i; j < i+m; j++) {
				a[j] = (a[j]+b[j-i])%c;
			}
		}
		for (int i = 0; i < n; i++) {
			System.out.print(a[i]+" ");
		}
	}

}
