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. 
n, m, c = map(int, raw_input().split())
a = map(int, raw_input().split())
b = map(int, raw_input().split())

i = 0

#print a, b

pre_sums = [b[0]]
for i in xrange(1,m):
    pre_sums.append((b[i] + pre_sums[i-1]) % c)

post_sums = [b[-1]]
for i in xrange(2,m+1):
    post_sums.insert(0, (b[-i] + post_sums[-i+1]) % c)

summa = pre_sums[-1]

#print summa, pre_sums, post_sums

i = 0
j = n - 1
count = 0
while i  < j :
    if i + m <= n:
        count += 1
        if i < m:
            a[i] = (a[i] + pre_sums[i]) % c
            a[j] = (a[j] + post_sums[-i-1]) % c
        else:
            a[i] = (a[i] + summa) % c
            a[j] = (a[j] + summa) % c
    else:
        a[i] = (a[i] + pre_sums[i] - pre_sums[i-count]) % c
        a[j] = (a[j] + post_sums[-i-1] - post_sums[-i-1+count]) % c
    i += 1
    j -= 1

if i == j + 1:
    print " ".join(map(str, a))
else:
    if i < m - 1:
        a[i] = (a[i] + sum(b[m-i-1:i+1])) % c
        print " ".join(map(str, a))
    else:
        a[i] = (a[i] + summa) % c
        print " ".join(map(str, a))