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:
import math
import collections
from itertools import permutations
from itertools import combinations
# import sys
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')


'''def is_prime(n):
    j=2
    while j*j<=n:
        if n%j==0:
            return 0
        j+=1
    return 1'''


'''def gcd(x, y):
    while(y):
        x, y = y, x % y
    return x'''


def prob():
    
    # n = int(input())
    # s=input()

    n,k=[int(x) for x in input().split()]
    l=[int(x) for x in input().split()]
    ans=[]

    for i in range(1,n*k+1):
        if i not in l:
            ans.append(i)

    for i in range(k):
        print(l[i] , *ans[i*(n-1) : (i+1)*(n-1)])
    

t=1
# t=int(input())

for _ in range(0,t):
    prob()