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.lang.reflect.Array;
import java.util.*;

public class Main {
    BufferedReader input;
    PrintWriter output;

    Main() {
        try {
            input = new BufferedReader(new FileReader("input.txt"));
            output = new PrintWriter(new FileWriter("output.txt"), true);
            solve();
        } catch (Exception ex) {
            ex.printStackTrace();
            input = new BufferedReader(new InputStreamReader(System.in));
            output = new PrintWriter(System.out, true);
            solve();
        } finally {
            try {
                input.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
            output.close();
        }
    }

    StringTokenizer st;

    String nextToken() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(input.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    double nextDouble() {
        return Double.valueOf(nextToken());
    }

    int nextInt() {
        return Integer.valueOf(nextToken());
    }

    public void solve() {
        int n = nextInt();
        int m = nextInt();
        int c = nextInt();
        int[] a = new int[n];
        int[] b = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        for (int i = 0; i < m; i++) {
            b[i] = nextInt();
        }
        int s = 0;
        for (int i = 0; i < n; i++) {
            if (i+m <= n) {
                if (i < m)
                    s += b[i];
            } else {
                    s = s + b[i] - b[i-n+m-1];
            }
            a[i] += s;
        }
        for (int i = 0; i < n; i++) {
            output.print(a[i] % c + " ");
        }
    }

    public static void main(String[] args) {
        new Main();
    }
}

class Pair {
    double x;
    double y;

    Pair(double x, double y) {
        this.x = x;
        this.y = y;
    }
}