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 PYTHON):

Solution:
import sys
import copy	
import os


def next(b, c, n):
	for i in range(c,n):
		if b[i] == 0:
			return i
	return -1

def main(cin):
	nv = map(int,cin.readline().strip().split())
	n = nv[0]
	k = nv[1]
	v = map(int, cin.readline().strip().split())
	b = [0 for i in range(k*n+1)]

	res = [[] for i in range(k)]

	for i in range(k):
		t = [str(v[i])]
		b[v[i]] = 1
		res[i] = t

	c = 1

	for i in range(k):
		for j in range(n-1):
			c = next(b,c,n*k+1)
			res[i].append(str(c))
			b[c] = 1

	for i in range(k):
		print ' '.join(res[i])


if __name__ == "__main__":
	cin = sys.stdin
	if (os.path.exists('best.txt')):
		cin = open('best.txt')
	main(cin)