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 implements Runnable {
		
	public void solve() throws IOException {
		int N = nextInt(); int M = nextInt(); int MOD = nextInt();
                long[] a  = new long[N];
                for(int i = 0; i < N; i++) a[i] = nextInt();

                long[] b = new long[M];
                for(int i = 0; i < M; i++) b[i] = nextInt();
                
                long[] bsum = new long[M+1];
                for(int i = 0; i < M; i++){
                        bsum[i+1] = (bsum[i] + b[i]) % MOD;
                }
                
                for(int i = 0; i < N; i++){
                    int start = -1, end = -1; //right, left
                    if(i < M){
                        start = i+1;
                        end = start - (N-M+1);
                        if(end < 0) end = 0;
                    }
                    else if(N-i < M){
                        start = M;
                        end = start - (N-i);
                        if(end < 0) end = 0;
                    }
                    else{
                        start = M;
                        end = start - (N-M);
                        if(end < 0) end = 0;
                    }
                    //System.out.println(start + " " + end);
                    a[i] = (a[i] + bsum[start] - bsum[end] + MOD) % MOD;
                }
                
                StringBuilder ans = new StringBuilder();
                for(int i = 0; i < N; i++) ans.append(" " + a[i]);
                
                System.out.println(ans.toString().substring(1));
	}

	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	//-----------------------------------------------------------
	public static void main(String[] args) {
		new Main().run();
	}

        public void print1Int(int[] a){
                for(int i = 0; i < a.length; i++)
                        System.out.print(a[i] + " ");
                System.out.println();
        }
        
        public void print2Int(int[][] a){
                for(int i = 0; i < a.length; i++){
                        for(int j = 0; j < a[0].length; j++){
                                System.out.print(a[i][j] + " ");
                        }
                        System.out.println();
                }
        }
        
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			tok = null;
			solve();
			in.close();
		} catch (IOException e) {
			System.exit(0);
		}
	}

	public String nextToken() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}

	public int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	public long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}

	BufferedReader in;
	StringTokenizer tok;
}