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.util.*;
import java.io.*;

public class prob {
    
    static Scanner sc;
    static PrintWriter pw;
    static int[][] a;
    static int n, m, c;
    static Set[] set = new HashSet[2000];
    
    
    public static void main(String[] args) {
        sc = new Scanner(System.in);
        pw = new PrintWriter(System.out);
        try{
            n = sc.nextInt();
            m = sc.nextInt();
            c = sc.nextInt();
            int[] a = new int[n];
            int[] b = new int[m];
            int[] s = new int[m];
            long sum = 0;
            for(int i = 0; i < n; i++)
                a[i] = sc.nextInt();
            for(int i = 0; i < m; i++)
                b[i] = sc.nextInt();
            s[0] = b[0];
            for(int i = 1; i < m; i++) 
                s[i] = (s[i - 1] + b[i]) ;
            if(n / 2 >= m) {
                for(int i = 0; i < m; i++)
                    a[i] = (a[i] + s[i]) ;
                for(int i = m ; i <= n - m; i++)
                    a[i] = (a[i] + s[m - 1]);
                for(int i = n - m + 1, k = 0 ; i < n; i++, k++)
                    a[i] = (a[i] + s[m - 1] - s[k]) ;
            } else {
                int r = n - m;
                for(int i = 0; i <= r; i++)
                    a[i] = (a[i] + s[i]);
                for(int i = r + 1; i < n - r ; i++)
                    a[i] = (a[i] + s[i] - ((i - r - 1) < 0 ? 0 : s[i - r - 1]) );    
                for(int i = n - r; i < n; i++) 
                    a[i] = (a[i] + s[m - 1]);
                for(int i = n - 1, k = m - 2; i >= n - r; i--, k--)
                    a[i] = (a[i] - s[k]);
                
            }
            for(int i = 0; i < n; i++)
                pw.print(a[i] % c + " ");
        }
        finally {
            pw.close();
        }
    }
}
