It was a dark and dreary Christmas Eve when our hero pondered, weak and weary, over a quaint and curious COCI task. When he nodded, nearly napping, suddenly he heard a tapping, tapping and a mighty roar. A giant reindeer broke through his chamber door, merely this and nothing more. While our hero's heart slightly fluttered, the beast simply uttered: "I won't leave until you solve this problem".

In the problem, you were given two integers ~N~ and ~M~ and you were supposed to perfectly match the numbers from sets ~A = \{0, 1, 2, \dots, N-1\}~ and ~B = \{M, \dots, M+N-1\}~ into ~N~ pairs, such that for the matched numbers ~x \in A~ and ~y \in B~ it holds ~x \mathbin{\&} y = x~, where ~\&~ denotes a bitwise AND operation.

Input

The first line contains two integers ~N~ and ~M~ ~(1 \le N \le M, N+M \le 10^6)~ from the task description.

Output

You should output ~N~ lines and in each line you should output two integers ~x~ and ~y~, where ~x~ belongs to set ~A~ and ~y~ belongs to set ~B~. Numbers in each line should correspond to one of the matched pairs from the task description.

It is possible to prove that the solution always exists.

Scoring

Subtask	Score	Constraints
~1~	~10~	~N~ is a power of ~2~
~2~	~29~	~N+M~ is a power of ~2~
~3~	~39~	~N+M \le 1000~
~4~	~32~	No additional constraints.

Sample Input 1

1 3

Sample Output 1

0 3

Sample Input 2

3 5

Sample Output 2

0 5
1 7
2 6

Sample Input 3

5 10

Sample Output 3

0 12
1 13
2 10
3 11
4 14