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.*;
import java.util.*;
public class GelMat{
    public static void main(String[] args){	
	int n=0;// size of matrix	
	int m=0;
	int c=0;
	int middle=0;
//	System.out.println("Enter the range of matrix, it should be odd");
	Scanner in=new Scanner(System.in);
	n=in.nextInt();
	m=in.nextInt();	
	while (m>n){
//	    System.out.println("The value should be odd");
	    m=in.nextInt();
	};
	c=in.nextInt();
	int[] A=new int[n];
	int[] B=new int[m];
	for(int i=0;i<n;i++){
	    A[i]=in.nextInt();
	    while((A[i]>(c-1))||(A[i]<0)){
	        A[i]=in.nextInt();		
	    }
	};
	for(int i=0;i<m;i++){
	    B[i]=in.nextInt();
	    while((B[i]>(c-1))||(B[i]<0)){
	        B[i]=in.nextInt();		
	    }
	    
	};

	for(int i=0;i<(n-m+1);i++){
	    for(int j=0;j<m;j++){
	     A[j+i]=(A[j+i]+B[j])%c;
	    }
	}
	for (int j=0;j<n;j++){
		System.out.print(A[j]+" ");	
	}
//System.out.println(sumEl);         
//	
    }
}