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;


public class EncryptionMessage 
{
public static void main(String[] args) {
	Scanner sc=new Scanner(System.in);
	int n=sc.nextInt();
	int m=sc.nextInt();
	int c=sc.nextInt();
	int total=n-m+1;
	int i=1;
	int na[]=new int[n];
	int ma[]=new int[m];
	while(i<=n)
	{
		na[i-1]=sc.nextInt();
	++i;
	}
i=1;
while(i<=m)
{
	ma[i-1]=sc.nextInt();
	++i;
}
i=1;
int pos=0,k=0,curr;
while(i<=total)
{
	k=0;
	for(int j=1;j<=m;j++)
	{
		curr=na[pos+k]+ma[j-1];
		na[pos+k]=curr%c;
		++k;
	}
	++i;
	++pos;
}

for(int p=0;p<n;p++)
	System.out.print(na[p]+" ");


}
}
