Chemistry

Vasya attends his Chemistry classes. During the latest semester, his group has been studying dry liquids. In a lab session on mixing liquids, Vasya received oxygen oxide. This substance has unpredictable consequences after mixing. The liquid is stable only when it is mixed in a one-to-one ratio.

Vasya has $n$ test tubes, and each one contains 1 nanoliter of oxygen oxide. Because of the properties of the oxide, Vasya pours liquid from test tube $A$ into test tube $B$ so that the resulting volume in test tube $B$ doubles. To make the experiment succeed, Vasya needs exactly $k$ nanoliters of oxide in one of the test tubes. Help him do this.

The only line contains two integers $n$ and $k$ ($1 ≤ n ≤ 100000$, $1 ≤ k ≤ n$).

Output the sequence of pours that leaves exactly $k$ nanoliters of oxide in the first test tube.

On the first line, output the number of pours $m$ ($0 ≤ m ≤ 3n$). Then output $m$ lines, each with two integers $a$ and $b$ ($1 ≤ a, b ≤ n$), meaning Vasya pours oxide from test tube $a$ into test tube $b$.

If no such sequence exists, output -1. If several solutions exist, output any of them. It is guaranteed that if a sequence exists, one exists with at most $3n$ pours.