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.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.List;
import java.util.Set;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    StringTokenizer str = null;
    BufferedReader in;
    PrintWriter out;

    void run() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(new OutputStreamWriter(System.out));
        solve();
        out.flush();
        out.close();
    }

    String nextString() throws IOException {
        return in.readLine();
    }

    String nextToken() throws IOException {
        if (str == null || !str.hasMoreElements()) {
            str = new StringTokenizer(nextString());
        }
        return str.nextToken();
    }

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

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

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

    void solve() throws IOException {
        int n = nextInt();
        int m = nextInt();
        long c = nextInt();
        long a[] = new long[n];
        long b[] = new long[m];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        b[0] = nextInt();
        for (int i = 1; i < m; i++) {
            b[i] = b[i - 1] + nextInt();
        }
        if (n == m) {
            for (int i = 0; i < n; i++) {
                long k = (a[i] + b[i] - ((i > 0) ? b[i - 1] : 0)) % c;
                out.print(k);
                out.print(" ");
            }
            return;
        }
        int f = n - m + 1;
        if (m > f) {
            for (int i = 0; i < f; i++) {
                long k = (a[i] + b[i]) % c;
                out.print(k);
                out.print(" ");
            }
            int p = f;
            for (int i = f; i < n - f + 1; i++) {
                long k = (a[i] + b[p] - b[p - f]) % c;
                p++;
                out.print(k);
                out.print(" ");
            }
            int d = m - f;
            for (int i = n - f + 1; i < n; i++) {
                long k = (a[i] + b[m - 1] - b[d++]) % c;
                out.print(k);
                out.print(" ");
            }
        } else {
            for (int i = 0; i < m - 1; i++) {
                long k = (a[i] + b[i]) % c;
                out.print(k);
                out.print(" ");
            }
            for (int i = m - 1; i < n - (m - 2) - 1; i++) {
                long k = (a[i] + b[m - 1]) % c;
                out.print(k);
                out.print(" ");
            }
            int d = 0;
            for (int i = n - m + 1; i < n; i++) {
                long k = (a[i] + b[m - 1] - b[d++]) % c;
                out.print(k);
                out.print(" ");
            }
        }
    }
}