Problem: One day Ms Swan bought an orange in a shop. The orange consisted of n·k segments, numbered with integers from 1 to n·k. 

There were k children waiting for Ms Swan at home. The children have recently learned about the orange and they decided to divide it between them. For that each child took a piece of paper and wrote the number of the segment that he would like to get: the i-th (1 ≤ i ≤ k) child wrote the number ai (1 ≤ ai ≤ n·k). All numbers ai accidentally turned out to be different.

Now the children wonder, how to divide the orange so as to meet these conditions:

  * each child gets exactly n orange segments; 
  * the i-th child gets the segment with number ai for sure; 
  * no segment goes to two children simultaneously. 



Help the children, divide the orange and fulfill the requirements, described above.

Input

The first line contains two integers n, k (1 ≤ n, k ≤ 30). The second line contains k space-separated integers a1, a2, ..., ak (1 ≤ ai ≤ n·k), where ai is the number of the orange segment that the i-th child would like to get.

It is guaranteed that all numbers ai are distinct.

Output

Print exactly n·k distinct integers. The first n integers represent the indexes of the segments the first child will get, the second n integers represent the indexes of the segments the second child will get, and so on. Separate the printed numbers with whitespaces.

You can print a child's segment indexes in any order. It is guaranteed that the answer always exists. If there are multiple correct answers, print any of them.

Examples

Input

2 2
4 1


Output

2 4 
1 3 


Input

3 1
2


Output

3 2 1 

Solution (in PYTHON3):

Solution:
def inp():
    return map(int, input().split())


def arr_inp():
    return [int(x) for x in input().split()]


def print_arr(arr):
    print(*arr, sep=' ')


n, k = inp()
a = arr_inp()
extra, len, old,c = [], 0, 0, 0

for i in range(1, n * k + 1):
    if (i not in a):
        extra.append(i)
        len += 1

    if (len > 0 and len % (n - 1) == 0 and len > old):
        ix1, ix2 = c*(n-1), len
        print(a[c], end=' ')
        print_arr(extra[ix1:ix2])
        old = len
        c+=1

    if(n==1):
        print(a[i-1])