Given the complete bipartite graph with the number of vertices in two distinct subsets are ~n~ and ~m~. Output the list of edges in the lexicographic order

Input

• The first line contains two integers ~n, m~ ~(0 < n, m ≤ 10^3)~.
• The second line contains ~n~ distinct integers ~a_i~ ~(0 ≤ a_i ≤ 10^9)~ that represent vertices of the first subset
• The second line contains ~m~ distinct integers ~b_j~ ~(0 ≤ b_j ≤ 10^9)~ that represent vertices of the second subset.
  • ~50\%~ of test cases has ~(0 ≤ a_i ≤ n-1, n ≤ b_j ≤ n+m-1)~.
  • ~90\%~ of test cases has ~(0 ≤ a_i, b_j ≤ n+m-1)~.

Output

• Output the edges of the graph in lexicographic order.

Sample Input 1

3 2
0 3 1
4 2

Sample Output 1

0 2
0 4
1 2
1 4
2 3
3 4

Sample Input 2

3 2
0 1 2
3 4

Sample Output 2

0 3
0 4
1 3
1 4
2 3
2 4