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
{
	public static void main(String[] args)throws Exception
	{
	    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	    PrintWriter pw=new PrintWriter(System.out);
	    String s[]=(br.readLine()).split(" ");
	    int n=Integer.parseInt(s[0]);
	    int m=Integer.parseInt(s[1]);
	    int c=Integer.parseInt(s[2]);
	    String s1[]=(br.readLine()).split(" ");
	    int a[]=new int[n];
	    for(int i=0;i<n;i++)
	    {
	        a[i]=Integer.parseInt(s1[i]);
	    }
	    String s2[]=(br.readLine()).split(" ");
	    int b[]=new int[m];
	    int bs[]=new int[m];
	    
	    for(int i=0;i<m;i++)
	    {
	        b[i]=Integer.parseInt(s2[i]);
	    }
	    bs[0]=b[0];
	    for(int i=1;i<m;i++)
	    {
	        bs[i]=bs[i-1]+b[i];
	    }
	    int moves=n-m+1;
	    int x=moves;
	    int xx=0;
	    for(int i=0;i<=m-2;i++)
	    {
	        if(x>0)
	        {
	            a[i]+=bs[i];
	            x--;
	        }
	        else
	        {
	            a[i]+=bs[i]-bs[xx];
	            xx++;
	        }
	    }
	    int in=m-1;
	    int temp=0;
	    x=Math.min(moves,m-1);
	    for(int i=n-1;/*i>=n-m+1*/;i--)
	    {
	        if(x>0)
	        {
	            temp+=b[in];
	            a[i]+=temp;
	            in--;
	            x--;
	        }
	        else
	        {
	            break;
	        }
	        
	        
	        
	    }
	    for(int i=m-1;i<=n-m;i++)
	    {
	        a[i]+=bs[m-1];
	    }
	    
	    for(int i=0;i<n;i++)
	    {
	        a[i]%=c;
	    }
	    for(int i=0;i<n;i++)
	    {
	        pw.print(a[i]+" ");
	    }
	    pw.println();
	    pw.flush();
	}
}
