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.FileNotFoundException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

/**
 *
 *
 *
 *
 *
 * @author pttrung
 */
public class D {

    public static long MOD = 100000000;

    public static void main(String[] args) throws FileNotFoundException {
        PrintWriter out;

        Scanner in = new Scanner();
        //out = new PrintWriter(new FileOutputStream(new File("output.txt")));
        out = new PrintWriter(System.out);
        int n = in.nextInt();
        int m = in.nextInt();
        int c = in.nextInt();
        int[] data = new int[n];
        for (int i = 0; i < n; i++) {
            data[i] = in.nextInt();
        }
        int[] other = new int[n];
        for (int i = 0; i < m; i++) {
            other[i] = in.nextInt();
        }
        int[] dp = new int[m];
        dp[0] = other[0] % c;
        for (int i = 1; i < m; i++) {
            dp[i] = other[i] + dp[i - 1];
            dp[i] %= c;
        }
        /**
         * 20 15 17 4 9 14 11 15 16 15 4 0 10 7 12 10 1 8 6 7 14 1 13 6 3 14 8 8
         * 11 16 4 5 9 2 13 6 14 15
         */
        for (int i = 0; i < n; i++) {
            if (i >= m - 1 && n - i > m - 1) {
                data[i] += dp[m - 1];
                data[i] %= c;
            } else if (i <= n - m) {
                //System.out.println(i);
                data[i] += dp[i];
                data[i] %= c;

            } else if (i < m - 1) {
                //  System.out.println(i);
                data[i] += dp[i] - dp[m - (n - i + 1)];
                data[i] %= c;
                while (data[i] < 0) {
                    data[i] += c;
                }
            } else {
                //System.out.println(i + " " + (m - (n - i + 1)));
                data[i] += dp[m - 1] - dp[m - (n - i + 1)];
                data[i] %= c;
                while (data[i] < 0) {
                    data[i] += c;
                }
            }
            out.print(data[i] + " ");
        }
        out.close();

    }

    public static class FT {

        int[] data;

        FT(int n) {
            data = new int[n];
        }

        public void update(int index, int value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public int get(int index) {
            int result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static class Sign {

        char c;
        int x, y;

        public Sign(char c, int x, int y) {
            this.c = c;
            this.x = x;
            this.y = y;
        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val % MOD;
        } else {
            return val * (val * a % MOD) % MOD;
        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}
