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.Scanner;

public class D {
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);

		int n = s.nextInt();
		int m = s.nextInt();
		int c = s.nextInt();

		int lines = n - m + 1;

		int[] a = new int[n];
		int[] b = new int[m];

		for (int i = 0; i < n; ++i) {
			a[i] = s.nextInt();
		}

		int[] first = new int[m];
		int[] last = new int[m];

		int summ = 0;
		int fs = summ;

		for (int i = 0; i < m; ++i) {
			b[i] = s.nextInt();
			summ = (summ + b[i]) % c;

			if (i < lines) {
				fs = summ;
			} else {
				fs = (fs + b[i] + c - b[i - lines]) % c;
			}

			first[i] = fs;

			// int minLine = Math.max(i - lines + 1, 0);
			// for (int j = i; j >= minLine; --j) {
			// first[i] = (first[i] + b[j]) % c;
			// }
		}

		if (m == 1) {
			m1(a, b[0], c, n);
			return;
		}

		if (m == n) {
			mn(a, b, c, n);
			return;
		}

		int tmp = summ;
		last[0] = tmp;

		for (int i = 1; i < m; ++i) {
			tmp = (tmp + c - b[i - 1]) % c;
			last[i] = tmp;
		}

		// for (int i = 0; i < m; ++i) {
		// System.out.print(first[i] + " ");
		// }
		//
		// System.out.println();
		//
		// for (int i = 0; i < m; ++i) {
		// System.out.print(last[i] + " ");
		// }

		java.io.PrintStream o = System.out;

		for (int i = 0; i < m; ++i) {
			o.print((a[i] + first[i]) % c);
			o.print(' ');
		}

		// blya

		int mm = m;
		int tail = n - m;

		if (tail > m - 1) {
			for (int i = m; i <= tail; ++i) {
				o.print((a[i] + last[0]) % c);
				o.print(' ');
			}

			mm = tail + 1;
			tail = m - 1;
		}

		for (int i = mm; i < n; ++i) {
			o.print((a[i] + last[m - tail + (i - mm)]) % c);
			o.print(' ');
		}
	}

	private static void mn(int[] a, int[] b, int c, int n) {
		java.io.PrintStream o = System.out;
		for (int i = 0; i < n; ++i) {
			o.print((a[i] + b[i]) % c);
			o.print(' ');
		}
	}

	private static void m1(int[] a, int b, int c, int n) {
		java.io.PrintStream o = System.out;
		for (int i = 0; i < n; ++i) {
			o.print((a[i] + b) % c);
			o.print(' ');
		}
	}
}
