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.*;
import java.math.*;

public class P177D {

  public PrintWriter run() {
    int n = sc.nextInt();
    int m = sc.nextInt();
    int c = sc.nextInt();
    int [] a = new int [n];
    int [] b = new int [m];
    for (int i = 0; i < n; i++) { a[i] = sc.nextInt(); }
    for (int i = 0; i < m; i++) { b[i] = sc.nextInt(); }

    long s = 0;
    int idx2 = 0;
    int idx3 = 0;

    for (int idx1 = 0; idx1 < n; idx1++)  {
      if (idx1 < m) {
        s += b[idx2];
        idx2++;
      }
      if (idx1 > (n - m)) {
        s -= b[idx3];
        idx3++;
      }
      a[idx1] = (int)(((long)a[idx1] + s) % c);
    }

    for (int aa : a) {
      pw.print(aa + " ");
    }
    pw.println();

    return pw;
  }

  private Scanner sc = new Scanner(new BufferedInputStream(System.in));
  private PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out));

  public static void main(String... args) throws Exception {
    new P177D().run().close();
  }
}
