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 MyClass { 
    	public static int a[];
    	public static int b[];
        public static void main(String[] args) {
        	Scanner sc=new Scanner(System.in);
        	long t=1;
        	while(t-->0) {
        		int n=sc.nextInt();
        		int m=sc.nextInt();
        		int c=sc.nextInt();
        		int sum=0;
        		a=new int[n+5];
        		b=new int[n+5];
        		Queue<Integer>q=new LinkedList<Integer>();
        		for(int i=1;i<=n;i++) {
        			a[i]=sc.nextInt();
        		}
        		for(int i=1;i<=m;i++) {
        			b[i]=sc.nextInt();
        		}
        		if(m<(n/2)+1) {
        			for(int i=1;i<=n;i++) {
        				if(i>=n-m+2) {
        					int temp=q.peek();
        					q.remove();
        					sum-=temp;
        				}else {
        					if(q.size()<m) {
        						sum+=b[i];
        						q.add(b[i]);
        					}
        				}
        				System.out.print((sum+a[i])%c+" ");
        			}
        		}else {
        			for(int i=1;i<=n;i++) {
        				if(i>=m+1) {
        					int temp=q.peek();
        					q.remove();
        					sum-=temp;
        				}else {
        					if(q.size()<n-m+1) {
        						sum+=b[i];
        						q.add(b[i]);
        					}else if(q.size()==n-m+1) {
        						int temp=q.peek();
        						q.remove();
        						sum-=temp;
        						q.add(b[i]);
        						sum+=b[i];
        					}
        				}
        				System.out.print((sum+a[i])%c+" ");
        			}
        		}
        	}
        }
    }
    