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 EncryptingMessages
{

	public static void main(String args[])throws IOException
	{
		
		FastReader sc= new FastReader();
		PrintWriter out = new PrintWriter(System.out);

		int tc,i,j;
		String s;char p;

		tc=1;
		while(tc-->0){
            int n=sc.nextInt();
            int m=sc.nextInt();
            int c= sc.nextInt();
            int arr[]=sc.readArray(n);
            int b[]= sc.readArray(m);
            int temp;
            for (i = 0; i < n-m+1; i++) {
                temp=i;
                for (j = 0; j <m ; j++){
                    arr[temp]=(b[j]+arr[temp])%c;
                    temp++;
                }
            }

            for (int item:arr)
                out.print(item+" ");
        }
		out.close();
	}
	





	/*
		FASTREADER
	*/
	static class FastReader 
    	{ 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
	
		/*DEFINED BY ME*/
		
		//READING ARRAY
		int[] readArray(int n){
			int arr[]=new int[n];
			for(int i=0;i<n;i++)
				arr[i]=nextInt();
			return arr;
		}
		//COLLECTIONS SORT
		 void sort(int arr[]){
            ArrayList<Integer> l=new ArrayList<>();
            for (int i: arr)
                l.add(i);
            Collections.sort(l);
            for (int i = 0; i < arr.length; i++)
                arr[i]=l.get(i);
        }
        //EUCLID'S GCD
        int gcd (int a , int b){
            if(b!=0)
                return gcd (b , a%b);
            else
                return a;
        }
    } 
}