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.StringTokenizer;

public class D2 {

    
    public static void main(String[] args) throws IOException {
        FastReader in= new FastReader();
     int n=in.nextInt();
     int m=in.nextInt();
     int c=in.nextInt();
     int a[]= new int[n];
     int b[]= new int[m];
        for (int i = 0; i < a.length; i++) {
            a[i]=in.nextInt();
        }
         for (int i = 0; i < b.length; i++) {
            b[i]=in.nextInt();
        }
     int k=0;
        for (int i = 0; i <=n-m; i++) {
            int y=k;
            int r=0;
            for (int j = y; j < k+b.length; j++) {
                a[j]=(b[r++]+a[j])%c;
            }
            k++;
        }
        for (int i = 0; i < a.length; i++) {
            System.out.print(a[i]+" ");
        }
        
        
    }
    
}


class FastReader {

        StringTokenizer st;
        BufferedReader br;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public boolean hasNext() throws IOException {
            String s = br.readLine();
            if (s == null || s.isEmpty()) {
                return false;
            }
            st = new StringTokenizer(s);
            return true;
        }

        public String next() throws IOException {
            if (st == null || !st.hasMoreTokens()) {
                String s = br.readLine();
                if (s.isEmpty()) {
                    return null;
                }
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }
    }

