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:
# recebe e converte a primeira linha
n = input()
n,k = n.split()
n = int(n)
k = int(k)

# recebe e converte a segunda linha
i = input()
numeros=[]
numeros=i.split()
for i in range(k):
     numeros[i] = int(numeros[i])

laranja=[-1 for i in range(n*k+1)]

# setar os numeros que os meninos pediram para dentro da lista laranja
for i in range(k):
    laranja[numeros[i]]=i


count=n-1
for i in range(k):  #para cada criança
    for j in range(1,n*k+1):
        if laranja[j]== -1:
            laranja[j]=i
            count-=1
        if count==0:
            count=n-1
            break

for j in range(k):
    for i in range(1,n*k+1):
        if laranja[i]==j:
            print(i, " ", end="")
    print()