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.*;
import java.util.*;

public class Task {

	public static void main(String[] args) throws Exception {
		new Task().solve();
	}
	
	void solve() throws Exception {
		Reader in = new Reader();
		PrintWriter out = new PrintWriter(new BufferedWriter(
		new OutputStreamWriter(System.out)));
		int n = in.nextInt();
		int m = in.nextInt();
		int c = in.nextInt();
		long a[] = new long[n];
		long b[] = new long[n];
		for (int i = 0; i < n; i++) {
			a[i] = in.nextInt();
		}
		for (int i = 0; i < m; i++) {
			b[i] = in.nextInt();
		}
		long sum = 0;
		for (int i = 0; i < n; i++) {
			if (i+m <= n)
				sum += b[i];
			else
				sum = sum + b[i] - b[i-n+m-1];
			a[i] = (a[i] + sum) % c;
		}
		for (int i = 0; i < n; i++) {
			System.out.print(a[i] + " ");
		}
		// BufferedWriter out = new BufferedWriter( new
		// OutputStreamWriter(System.out) );
		out.flush();
		out.close();
	}

	class Reader {

		BufferedReader br;
		StringTokenizer token;

		Reader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String Next() throws Exception {
			while (token == null || !token.hasMoreElements()) {
				token = new StringTokenizer(br.readLine());
			}

			return token.nextToken();

		}

		int nextInt() throws Exception, Exception {
			return Integer.valueOf(Next());
		}

		long nextLong() throws Exception, Exception {
			return Long.valueOf(Next());
		}

		String nextString() throws Exception {
			return br.readLine();
		}

	}

}
