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.*;

public class ABBY_2_d {
	
	
	public static void main(String args[]){
		Scanner in=new Scanner(System.in);
		int n = in.nextInt(); int m = in.nextInt(); int c = in.nextInt();
		long a[]=new long[n];
		for (int i=0; i<n; i++) a[i] = in.nextInt();
		long b[]=new long[m];
		for (int i=0; i<m; i++) b[i]=in.nextInt();
		long d[]=new long[m];
		
		//for (int i=1; i<m; i++) b[i] += b[i-1];
		//for (int i=0; i<m; i++) System.out.print(b[i] + " ");
		for (int i = 0; i<n-m+1; i++){
			for (int j=0; j < m && j+i < n; j++)
				a[j+i]+=b[j]; 
			/*System.out.println(i + " " + (b[n-m]));
			if (i > n-m){a[i] += b[n-m]; } 
			else
			if (i < m) a[i] += b[i];
			else a[i] = b[m-1];*/
		}
		//for (int i=0; i<n; i++) System.out.print(a[i] + " ");
		for (int i=0; i<n; i++) a[i]%=c;
		for (int i = 0; i<n; i++)System.out.print(a[i] + " ");
		
	}

}
