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.*;
import java.io.*;

public class Main {
    
    BufferedReader in;
    StringTokenizer str = null;
    PrintWriter out;
    
    private String next() throws Exception{
	while (str == null || !str.hasMoreElements())
	    str = new StringTokenizer(in.readLine());
	return str.nextToken();
    }
    
    private int nextInt() throws Exception{
	return Integer.parseInt(next());
    }
    
    private long nextLong() throws Exception{
	return Long.parseLong(next());
    }
    
    private double nextDouble() throws Exception{
	return Double.parseDouble(next());
    }
    
    LazySemgemtTree tree;
    public void run() throws Exception{
	in =  new BufferedReader(new InputStreamReader(System.in));
	out = new PrintWriter(System.out);
	int n = nextInt(), m = nextInt(), mod = nextInt();
	int []a = new int[n];
	for(int i=0;i<n;i++) a[i] = nextInt();
	int []b = new int[m];
	for(int i=0;i<m;i++) b[i] = nextInt();
	
	tree = new LazySemgemtTree(a, mod);
	
	for(int i=0;i<m;i++){
	    tree.add(1, 0, n-1, i, n - m + i, b[i]);
	}
	for(int i=0;i<n;i++){
	    out.print(tree.get(1, 0, n-1, i) + " ");
	}
	out.println();
	out.close();
    }

    class LazySemgemtTree{
	int []tree;
	int mod;
	public LazySemgemtTree(int a[], int mod){
	    this.mod = mod;
	    int n = a.length;
	    int N = Integer.highestOneBit(n) << 2;
	    tree = new int[N];
	    build(1, 0, n-1, a);
	}

	private void build(int v, int tl, int tr, int []a){
	    if (tl == tr){
		tree[v] = a[tl];
		return;
	    }
	    int tm = (tl + tr) >> 1;
	    build(2*v, tl, tm, a);
	    build(2*v+1, tm+1, tr, a);
	}

	public void add(int v, int tl, int tr, int l, int r, int d){
	    if (l > r) return;
	    if (tl == l && tr == r){
		tree[v]+=d;
		tree[v]%=mod;
		return;
	    }
	    int tm = (tl + tr) >> 1;
	    add(2*v, tl, tm, l, Math.min(tm, r), d);
	    add(2*v+1, tm+1, tr, Math.max(l, tm+1), r, d);
	}

	public int get(int v, int tl, int tr, int pos){
	    if (tl == tr){
		return tree[v];
	    }
	    int tm = (tl + tr) >> 1;
	    if (tm >= pos) return (tree[v] + get(2*v, tl, tm, pos)) % mod;
	    return (tree[v] + get(2*v+1, tm+1, tr, pos)) % mod;
	}
    }
    
    public static void main(String[] args) throws Exception{
	new Main().run();
    }
}
