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. 
//package com.pb.codeforces.practice;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class CF177D2 {

	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
	
	public static void main(String[] args) {
		FastReader in = new FastReader();
		PrintWriter out = new  PrintWriter(System.out);
		int n = in.nextInt(); int m = in.nextInt(); int c = in.nextInt();
		long[] arr = new long[n];
		long[] k = new long[m];
		for(int i=0; i<n; i++)
			arr[i] = in.nextLong();
		for(int i=0; i<m; i++)
			k[i] = in.nextLong();
		long[] psum = new long[m];
		psum[0] = k[0];
		for(int i=1; i<m; i++)
			psum[i] = psum[i-1] + k[i];
		int steps = n - m + 1;
		int it = Math.min(m, steps);
		for(int i=0; i<it; i++) 
			arr[i] = (arr[i]%c + psum[i]%c)%c;
		for(int i=0; i<it; i++)
			arr[n-i-1] = (arr[n-1-i]%c + (psum[m-1] - ((m-1-i-1 < 0 ) ? 0 : psum[m-1-i-1]))%c)%c;
		int id = m - 2;
		for(int i=n-it-1; i>=it; i--) {
			if(it == m) arr[i] = (arr[i]%c + psum[m-1]%c)%c;
			else {
				arr[i] = (arr[i]%c + (psum[id] - psum[id-steps])%c)%c;
				id--;
			}
		}
		StringBuilder ans = new StringBuilder();
		for(int i=0; i<n; i++)
			ans.append(arr[i]+" ");
		out.println(ans);
		out.close();
	}
}
