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.

Difficulty: MEDIUM
Tags: Data structures
Skill types: Data structures

Starter code:

Solutions:
(n, m, c) = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
(s, k) = (0, n - m)
for i in range(n):
	if i < m:
		s += b[i]
	a[i] = (a[i] + s) % c
	if i >= k:
		s -= b[i - k]
print(' '.join((str(i) for i in a)))


(n, m, c) = map(int, input().split())
N = list(map(int, input().split()))
M = list(map(int, input().split()))
SM = [0]
for v in M:
	SM += [SM[-1] + v]
answer = []
for (i, v) in enumerate(N):
	if i + len(M) < len(N):
		l = 0
	else:
		l = len(M) - len(N) + i
	if i < len(M):
		r = i
	else:
		r = len(M) - 1
	answer += [(N[i] + SM[r + 1] - SM[l]) % c]
print(' '.join(map(str, answer)))


from collections import defaultdict
for _ in range(1):
	(n, m, c) = map(int, input().split())
	a = list(map(int, input().split()))
	b = list(map(int, input().split()))
	cur_sum = 0
	ans = [0] * n
	for (i, j) in enumerate(a):
		if i < m:
			cur_sum += b[i]
			cur_sum %= c
		if n - i < m:
			cur_sum -= b[m - 1 - (n - i)]
			cur_sum %= c
		ans[i] = (j + cur_sum) % c
	print(' '.join([str(i) for i in ans]))


(n, m, c) = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
sum = 0
for i in range(n):
	if i < m:
		sum = (sum + b[i]) % c
	if i >= n - m + 1:
		sum = (c + sum - b[i - (n - m + 1)]) % c
	a[i] = (a[i] + sum) % c
print(' '.join(map(str, a)))


(len_message, len_key, mod) = map(int, input().split())
message = list(map(int, input().split()))
key = list(map(int, input().split()))
(sum, low, high) = (0, 0, 0)
result = message[:]
for i in range(len_message):
	if high < len_key:
		sum += key[high]
		high += 1
	if i + len_key > len_message:
		sum -= key[low]
		low += 1
	result[i] = (result[i] + sum) % mod
print(' '.join(map(str, result)))


(n, m, c) = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
pre = [0] * m
suf = [0] * (m + 1)
ans = [0] * n
lp = min(m, n - m + 1)
j = -2
for i in range(m):
	pre[i] = pre[i - 1] + b[i]
for i in range(m - 1, -1, -1):
	suf[i] = suf[i + 1] + b[i]
for i in range(lp):
	ans[i] = (a[i] + pre[i]) % c
if lp == m:
	for i in range(lp, n - lp):
		ans[i] = (a[i] + pre[lp - 1]) % c
else:
	for i in range(lp, n - lp):
		ans[i] = (a[i] + pre[i] - pre[i - lp]) % c
for i in range(n - 1, n - lp - 1, -1):
	ans[i] = (a[i] + suf[j]) % c
	j -= 1
print(*ans)