Problem Statement

Two segments $[L_1:R_1]$ and $[L_2:R_2]$ are said to intersect when $L_1 \leq R_2$ and $L_2 \leq R_1$ holds.

Consider the following problem $P$:

Input: N segments [L_1: R_1], \cdots, [L_N:R_N]
       L_1, L_2, \cdots, L_N, R_1, R_2, \cdots, R_N are pairwise distinct.
Output: the maximum number of segments that can be chosen so that no two of them intersect.

Takahashi has implemented a program that works as follows:

Sort the given segments in the increasing order of R_i and let the result be [L_{p_1}:R_{p_1}], [L_{p_2}:R_{p_2}], \cdots , [L_{p_N}:R_{p_N}].
For each i = 1, 2, \cdots , N, do the following:
  Choose [L_{p_i}:R_{p_i}] if it intersects with none of the segments chosen so far.
Print the number of chosen segments.

Aoki, on the other hand, has implemented a program that works as follows:

Sort the given segments in the increasing order of L_i and let the result be [L_{p_1}:R_{p_1}], [L_{p_2}:R_{p_2}], \cdots , [L_{p_N}:R_{p_N}].
For each i = 1, 2, \cdots , N, do the following:
  Choose [L_{p_i}:R_{p_i}] if it intersects with none of the segments chosen so far.
Print the number of chosen segments.

Given are integers $N$ and $M$. Construct an input for the problem $P$, consisting of $N$ segments, such that the following holds:

$$ (\text{The value printed by Takahashi's program}) - (\text{The value printed by Aoki's program}) = M $$

Constraints

• All values in input are integers.
• $1 \leq N \leq 2 \times 10^5$
• $-N \leq M \leq N$

Input

Input is given from Standard Input in the following format:

N M

Output

If there is no set of $N$ segments that satisfies the condition, print -1.

Otherwise, print $N$ lines as follows:

L_1 R_1
L_2 R_2
  \vdots
L_N R_N

Here, $[L_1:R_1], \cdots, [L_N:R_N]$ must satisfy the following:

• $1 \leq L_i < R_i \leq 10^9$
• $L_i \neq L_j$ ($i \neq j$)
• $R_i \neq R_j$ ($i \neq j$)
• $L_i \neq R_j$
• $L_1, \cdots , L_N , R_1, \cdots , R_N$ are integers (21:46 added)

If there are multiple answers, any of them will be accepted.

Be sure to print a newline at the end of the output.