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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Vector;


public class Main {

    /**
     * @param args
     * @throws IOException 
     * @throws NumberFormatException 
     */

    public static void main(String[] args) throws NumberFormatException, IOException {
        // TODO Auto-generated method stub
        BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out=new PrintWriter(System.out);
        String[] input=in.readLine().split(" ");
        int n=Integer.parseInt(input[0]);
        int m=Integer.parseInt(input[1]);
        int c=Integer.parseInt(input[2]);
        String[] mesStr=in.readLine().split(" ");
        String[] keyStr=in.readLine().split(" ");
        int[] mes=new int[n];
        int[] key=new int[m];
        int[] ksum=new int[m];
        long[] kres=new long[n];
        for(int i=0; i<n; i++){
            mes[i]=Integer.parseInt(mesStr[i]);
        }
        for(int i=0; i<m; i++){
            key[i]=Integer.parseInt(keyStr[i]);
        }
        kres[0]=key[0];
        int steps=n-m+1;
        int otr=Math.min(steps,m);
        
        for(int i=1; i<otr; i++){
            kres[i]=kres[i-1]+key[i];
        }
        for(int i=otr; i<m; i++){
            kres[i]=kres[i-1]+key[i]-key[i-otr];
        }
        for(int i=m; i<n-otr+1; i++){
            kres[i]=kres[i-1];
        }
        for(int i=n-otr+1; i<n; i++){
            kres[i]=kres[i-1]-key[i-(n-m+1)];
        }
        for(int i=0; i<n; i++){
            out.print((mes[i]+kres[i])%c+" ");
        }
        out.close();
    }

}
