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 Main {
  BufferedReader br;
  int n, m, c;
  int[] a, b, fb, st, ed;
  
  public void go() throws Exception {
    br = new BufferedReader(new InputStreamReader(System.in));
    
    String[] ss = br.readLine().split(" ");
    n = Integer.parseInt(ss[0]);
    m = Integer.parseInt(ss[1]);
    c = Integer.parseInt(ss[2]);
    
    a = new int[n];
    b = new int[m];
    ss = br.readLine().split(" ");
    for (int i = 0; i < n; i++)
      a[i] = Integer.parseInt(ss[i]);
    ss = br.readLine().split(" ");
    for (int i = 0; i < m; i++)
      b[i] = Integer.parseInt(ss[i]);
    
    fb = new int[m+1];
    fb[0] = 0;
    for (int i = 0; i < m; i++)
      fb[i+1] = fb[i] + b[i];
    
    st = new int[n];
    ed = new int[n];
    for (int i = 0; i < n; i++) {
      st[i] = Math.max(0, i - n + m);
      ed[i] = Math.min(m - 1, i);
    }
    
    for (int i = 0; i < n; i++) {
      a[i] += fb[ed[i]+1] - fb[st[i]];
      a[i] %= c;
    }
    
    System.out.print(a[0]);
    for (int i = 1; i < n; i++)
      System.out.print(" " + a[i]);
    System.out.println();
  }
  
  public static void main(String[] args) throws Exception {
    new Main().go();
  }
}
