D. Delivery
time limit per test
0.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

A long, long time ago, the Olympians resided in the idyllic Olympic village. The village was built in the form of a connected, undirected graph with $$$N$$$ houses (vertices) and $$$M$$$ roads (edges). Once every year, the Olympians gather in one of the houses and take part in a lavish feast.

Choosing which house to hold the feast in was not a straightforward task — instead of picking a house randomly, the Olympians were adamant that the inconvenience should be minimized. Since Olympians in every house were responsible for delivering food and gifts to the location of the feast, the inconvenience of holding the feast in house $$$i$$$ was defined to be the maximum number of roads that an Olympian travels along to reach house $$$i$$$, assuming everyone walks to the feast using the smallest possible number of roads.

Unfortunately, we still do not know much about the structure of the graph to this day. Careful inspection of an ancient scroll revealed a note which stated the largest and smallest inconvenience among all $$$N$$$ possible houses. Given these two numbers, can you reconstruct the layout of the Olympic village?

Input

The first and only line of input consists of two integers $$$X$$$ and $$$Y$$$ ($$$1 \le X, Y \le 100$$$), the largest and smallest inconvenience respectively.

Output

If there does not exist a graph with largest inconvenience $$$X$$$ and smallest inconvenience $$$Y$$$, output -1.

Otherwise, output a possible graph with largest inconvenience $$$X$$$ and smallest inconvenience $$$Y$$$. If there are multiple solutions, you may output any one of them.

On the first line, output two integers $$$N$$$ ($$$2 \le N \le 1000$$$) and $$$M$$$. Then output $$$M$$$ more lines, each containing two integers $$$u$$$ and $$$v$$$ ($$$1 \le u, v \le N$$$, $$$u \neq v$$$) denoting a road between house $$$u$$$ and house $$$v$$$. Multiple edges between the same pair of houses are not allowed.

It is guaranteed that if there exists a solution, there exists a solution with $$$2 \le N \le 1000$$$.

Examples
Input
4 2
Output
7 6
3 5
6 2
2 1
3 4
2 3
7 5
Input
8 13
Output
-1
Note

For the first sample output, the table below shows the inconvenience of holding the feast in each house:

HouseInconvenience
$$$1$$$$$$4$$$
$$$2$$$$$$3$$$
$$$3$$$$$$2$$$
$$$4$$$$$$2$$$
$$$5$$$$$$3$$$
$$$6$$$$$$4$$$
$$$7$$$$$$4$$$