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 $x\mathrm{\&}y=x$, where $\mathrm{\&}$ 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