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. 

/**
 * Write a description of class ABBYYC here.
 * 
 * @author (your name) 
 * @version (a version number or a date)
 */
import java.util.*;
public class ABBYYD
{
    public static void main(String args[])
    {
        Scanner S = new Scanner(System.in);
        int n = S.nextInt();
        int m = S.nextInt();
        int c = S.nextInt();
        int[] M = new int[n];
        int[] K = new int[m];
        int[] O = new int[n];
        int sum = 0;
        for(int i = 0; i < n; i++)
        {
            M[i] = S.nextInt();
            O[i] = M[i];
        }
        for(int j = 0; j < m; j++)
        {
            K[j] = S.nextInt();
            sum += K[j];
        }
        if(n > 2*m)
        {
        O[0] = (M[0] + K[0]) % c;
        System.out.print(O[0] + " ");
        int k = K[0];
        
        for(int i = 1; i < n; i++)
        {
            if(i < m - 1)
            {
                k = (k + K[i]);
                O[i] = (O[i] + k) % c;
                System.out.print(O[i] + " ");
            }
            else if(i <= n - m)
            {
                k = sum;
                O[i] = (O[i] + k) % c;
                System.out.print(O[i] + " ");
            }
            else
            {
                k = k - K[i - (n - m + 1)];
                O[i] = (O[i] + k);
                if(O[i] < 0)
                    O[i] += c;
                O[i] %= c;
                System.out.print(O[i] + " ");
            }
            
        }
    }
    else
    {
        int i = 0;
        while(i + m <= n)
        {
            for(int j = 0; j < m; j++)
            {
                O[i + j] += K[j];
                O[i + j] %= c;
            }
            i++;
        }
        for(i = 0; i < n; i++)
            System.out.print(O[i] + " ");
    }
                
    }
        
}
