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.*;


public class Solution {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer token = new StringTokenizer(reader.readLine());

        int n = Integer.parseInt(token.nextToken());
        int m = Integer.parseInt(token.nextToken());
        int c = Integer.parseInt(token.nextToken());
        int a[] = new int[n];
        int b[] = new int[m];

        token = new StringTokenizer(reader.readLine());
        for (int i = 0; i < a.length; i++) {
            a[i] = Integer.parseInt(token.nextToken());
        }

        token = new StringTokenizer(reader.readLine());
        for (int i = 0; i < b.length; i++) {
            b[i] = Integer.parseInt(token.nextToken());
        }

        int d[] = new int[n];
        int z[] = new int[m];
        d[0] = b[0];
        z[0] = b[0];

        for (int i = 1; i < n; i++) {
            if (i < m) {
                d[i] = d[i - 1] + b[i];
                z[i] = d[i];
            } else {
                d[i] = d[i - 1];
            }
        }

        for (int i = 0; i < m - 1; i++) {
            d[n - m + i + 1] -= z[i];
        }

        for (int i = 0; i < d.length; i++) {
            a[i] = (a[i] + d[i]) % c;

        }

        for (int anA : a) {
            System.out.print(anA + " ");

        }
    }
}
