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.util.Arrays;
import java.util.StringTokenizer;

public class ab4 {

    public static void debug(Object... obs)
    {
        System.out.println(Arrays.deepToString(obs));
    }

    public static void main(String[] args) throws Throwable
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer(br.readLine());
        int n=Integer.parseInt(st.nextToken());
        int m=Integer.parseInt(st.nextToken());
        int c=Integer.parseInt(st.nextToken());
        
        int a[]=new int[n];
        int b[]=new int[m];
        long pb[]=new long[m];
        st=new StringTokenizer(br.readLine());
        for(int i=0;i<n;i++)
        {
            a[i]=Integer.parseInt(st.nextToken());
        }
        st=new StringTokenizer(br.readLine());
        long su=0;
        for(int i=0;i<m;i++)
        {
            int bi=Integer.parseInt(st.nextToken());
            su=(su+bi)%c;
            pb[i]=su;
        }
        
        //debug(pb);
        
        for(int i=0;i<n;i++)
        {
            int s=Math.max(0, i - n + m);
            int e=Math.min(i, m-1);
            
            //debug(i,s,e);

            long mdl=0;
            if(s==0)
                mdl = pb[e]%c;
            else
                mdl = (pb[e]-pb[s-1])%c;
            
            if(mdl < 0)
                mdl = c + mdl;
            
            //debug(i,s,e,mdl);
            
            int md=(int)mdl;
            
            int k = (a[i]+md)%c;
            
            System.out.print(k);
            if(i!=n-1)
                System.out.print(" ");
        }
        System.out.println();
    }
}