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.io.*;
import java.util.*;
import static java.lang.Math.*;

public class ABBYY_Cup_2012_Div2_D implements Runnable {

	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	
	BufferedReader in;
	PrintWriter out;
	StringTokenizer tok;

	public static void main(String[] args) {
		new Thread(null, new ABBYY_Cup_2012_Div2_D(), "", 256 * (1L << 20)).start();
	}

	@Override
	public void run() {
		try {
			long startTime = System.currentTimeMillis();
			if (ONLINE_JUDGE) {
				in = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(System.out);
			} else {
				in = new BufferedReader(new FileReader("input.txt"));
				out = new PrintWriter("output.txt");
			}
			Locale.setDefault(Locale.US);
			tok = new StringTokenizer("");
			solve();
			in.close();
			out.close();
			long freeMemory = Runtime.getRuntime().freeMemory();
			long totalMemory = Runtime.getRuntime().totalMemory();
			long endTime = System.currentTimeMillis();
			System.err.println("Time = " + (endTime - startTime));
			System.err.println("Memory = " + ((totalMemory - freeMemory) >> 10));
		} catch (Throwable t) {
			t.printStackTrace(System.err);
			System.exit(-1);
		}
	}

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

	int readInt() throws IOException {
		return Integer.parseInt(readString());
	}

	long readLong() throws IOException {
		return Long.parseLong(readString());
	}

	double readDouble() throws IOException {
		return Double.parseDouble(readString());
	}
	
	void debug(Object... o) {
		if (!ONLINE_JUDGE) {
			System.err.println(Arrays.deepToString(o));
		}
	}

	/** http://pastebin.com/j0xdUjDn */
	static class Utils {

		private Utils() {}

		public static void mergeSort(int[] a) {
			mergeSort(a, 0, a.length - 1);
		}

		private static final int MAGIC_VALUE = 50;

		private static void mergeSort(int[] a, int leftIndex, int rightIndex) {
			if (leftIndex < rightIndex) {
				if (rightIndex - leftIndex <= MAGIC_VALUE) {
					insertionSort(a, leftIndex, rightIndex);
				} else {
					int middleIndex = (leftIndex + rightIndex) / 2;
					mergeSort(a, leftIndex, middleIndex);
					mergeSort(a, middleIndex + 1, rightIndex);
					merge(a, leftIndex, middleIndex, rightIndex);
				}
			}
		}

		private static void merge(int[] a, int leftIndex, int middleIndex, int rightIndex) {
			int length1 = middleIndex - leftIndex + 1;
			int length2 = rightIndex - middleIndex;
			int[] leftArray = new int[length1];
			int[] rightArray = new int[length2];
			System.arraycopy(a, leftIndex, leftArray, 0, length1);
			System.arraycopy(a, middleIndex + 1, rightArray, 0, length2);
			for (int k = leftIndex, i = 0, j = 0; k <= rightIndex; k++) {
				if (i == length1) {
					a[k] = rightArray[j++];
				} else if (j == length2) {
					a[k] = leftArray[i++];
				} else {
					a[k] = leftArray[i] <= rightArray[j] ? leftArray[i++] : rightArray[j++];
				}
			}
		}

		private static void insertionSort(int[] a, int leftIndex, int rightIndex) {
			for (int i = leftIndex + 1; i <= rightIndex; i++) {
				int current = a[i];
				int j = i - 1;
				while (j >= leftIndex && a[j] > current) {
					a[j + 1] = a[j];
					j--;
				}
				a[j + 1] = current;
			}
		}

	}

	// solution
	
	int MOD;
	
	void solve() throws IOException {
		int n = readInt();
		int m = readInt();
		MOD = readInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = readInt();
		}
		int[] b = new int[m];
		for (int j = 0; j < m; j++) {
			b[j] = readInt();
		}
		int[] s = new int[m];
		s[0] = b[0];
		for (int i = 1; i < m; i++){ 
			s[i] = (s[i-1] + b[i]) % MOD;
		}
		int[] ans = new int[n];
		for (int i = 0; i < n; i++) {
			int left = 0;
			if (n - i < m) {
				left = m + i - n;
			}
			int right = m - 1;
			if (i < m - 1) {
				right = i;
			}
			debug(left, right);
			ans[i] = (a[i] + sum(s, left, right)) % MOD;
		}
		for (int i = 0; i < n; i++) {
			out.print(ans[i]);
			out.print(" ");
		}
	}
	
	int sum(int[] s, int L, int R) {
		int ans = s[R];
		if (L > 0) {
			ans -= s[L-1];
			ans += MOD;
		}
		return ans % MOD;
	}

}
