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

public class D2 implements Runnable {

	private void Solution() throws IOException {
		int n = nextInt(), m = nextInt(), c = nextInt();
		int[] a = new int[n], b = new int[m];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		for (int i = 0; i < m; i++)
			b[i] = nextInt();
		SegmentTree tree = new SegmentTree(a);
		for (int i = 0; i < m; i++)
			tree.inc(i, n - m + i, b[i]);
		for (int i = 0; i < n; i++) {
			if (i != 0)
				print(" ");
			print(tree.getMin(i, i) % c);
		}
	}

	class SegmentTree {
		int n;
		long[] t, inc;

		public SegmentTree(int[] a) {
			n = Integer.highestOneBit(a.length) << 1;
			t = new long[n << 1];
			inc = new long[n << 1];
			for (int i = 0; i < a.length; i++)
				inc(i, i, a[i]);
		}

		long get(int i) {
			return t[i] + inc[i];
		}

		void set(int i, long x) {
			inc[i] += x;
		}

		void push(int i) {
			if (inc[i] != 0) {
				set(i * 2 + 1, inc[i]);
				set(i * 2 + 2, inc[i]);
				t[i] = get(i);
				inc[i] = 0;
			}
		}

		void inc(int i, int tl, int tr, int l, int r, long x) {
			if (r <= tl || tr <= l)
				return;
			if (l <= tl && tr <= r) {
				set(i, x);
				return;
			}
			push(i);
			int m = (tl + tr) >> 1;
			inc(i * 2 + 1, tl, m, l, r, x);
			inc(i * 2 + 2, m, tr, l, r, x);
			t[i] = Math.min(get(i * 2 + 1), get(i * 2 + 2));
		}

		void inc(int l, int r, long x) {
			inc(0, 0, n, l, r + 1, x);
		}

		long getMin(int i, int tl, int tr, int l, int r) {
			if (r <= tl || tr <= l)
				return Long.MAX_VALUE;
			if (l <= tl && tr <= r)
				return get(i);
			push(i);
			int m = (tl + tr) >> 1;
			return Math.min(getMin(i * 2 + 1, tl, m, l, r),
					getMin(i * 2 + 2, m, tr, l, r));
		}

		long getMin(int l, int r) {
			return getMin(0, 0, n, l, r + 1);
		}
	}

	public static void main(String[] args) {
		new D2().run();
	}

	BufferedReader in;
	PrintWriter out;
	StringTokenizer tokenizer;

	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			Solution();
			out.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(0);
		}
	}

	void print(Object... o) {
		for (int i = 0; i < o.length; i++) {
			if (i != 0)
				out.print(" ");
			out.print(o[i]);
		}
	}

	void println(Object... o) {
		for (int i = 0; i < o.length; i++) {
			if (i != 0)
				print(" ");
			print(o[i]);
		}
		print("\n");
	}

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

	long nextLong() throws NumberFormatException, IOException {
		return Long.parseLong(next());
	}

	double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(next());
	}

	String nextLine() throws IOException {
		return in.readLine();
	}

	String next() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens())
			tokenizer = new StringTokenizer(nextLine());
		return tokenizer.nextToken();
	}
}
