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.util.Scanner;

/**
 * @Author Mikhail Linkov
 * Date: 21.04.12
 */
public class ProblemD {
    public static void main(String [] args) {
        Scanner scanner = new Scanner(System.in);

        int n = scanner.nextInt();
        int m = scanner.nextInt();
        int c = scanner.nextInt();

        int [] a = new int[n];
        int [] b = new int[m];

        int [] sum = new int[m];

        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
        }

        for (int i = 0 ; i < m; i++) {
            b[i] = scanner.nextInt();

        }

        sum[0] = b[0];
        for (int i = 1; i < m; i++) {
            sum[i] += sum[i - 1] + b[i];
        }

        int [] d = new int[n];

        for (int i = 0; i < n; i++) {
            int f = 0;
            if (i >= m) {
                d[i] = a[i] + sum[m - 1];
                f = 1;
            }
            if (n - i < m) {
                d[i] -= sum[m - (n - i) - 1];
                if (f == 0) {
                    d[i] += a[i] + sum[i];
                }
                f = 1;
            }

            if (f == 1) {
                continue;
            }
            d[i] = a[i] + sum[i];

        }
        for (int i = 0; i < n; i++) {
            System.out.print(d[i] % c + " ");
        }

    }
}
