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.
• $1 \\leq N \\leq 2 \\times 10^5$
• $\-N \\leq M \\leq N$

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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.

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Sample Input 1

5 1

Sample Output 1

1 10
8 12
13 20
11 14
2 4

Let us call the five segments Segment $1$, Segment $2$, $\\cdots$, Segment $5$.

Takahashi's program will work as follows:

Rearrange the segments into the order Segment $5$, Segment $1$, Segment $2$, Segment $4$, Segment $3$. Choose Segment $5$. Skip Segment $1$ (because it intersects with Segment $5$). Choose Segment $2$. Skip Segment $4$ (because it intersects with Segment $2$). Choose Segment $3$.

Thus, Takahashi's program will print $3$.

Aoki's program will work as follows:

Rearrange the segments into the order Segment $1$, Segment $5$, Segment $2$, Segment $4$, Segment $3$. Choose Segment $1$. Skip Segment $5$ (because it intersects with Segment $1$). Skip Segment $2$ (because it intersects with Segment $1$). Choose Segment $4$. Skip Segment $3$ (because it intersects with Segment $4$).

Thus, Aoki's program will print $2$.

Here, we have $3 - 2 = 1 \\left(= M \\right)$, and thus these five segments satisfy the condition.

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Sample Input 2

10 -10

Sample Output 2

-1