Problem Statement

Two segments [L1​:R1​] and [L2​:R2​] are said to intersect when L1​≤R2​ and L2​≤R1​ holds.

Consider the following problem $P$:

Input: $N$ segments [L1​:R1​],⋯,[LN​:RN​]
       L1​,L2​,⋯,LN​,R1​,R2​,⋯,RN​ 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 Ri​ and let the result be [Lp1​​:Rp1​​],[Lp2​​:Rp2​​],⋯,[LpN​​:RpN​​].
For each $i=1,2,\cdots ,N$, do the following:
  Choose [Lpi​​:Rpi​​] 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 Li​ and let the result be [Lp1​​:Rp1​​],[Lp2​​:Rp2​​],⋯,[LpN​​:RpN​​].
For each $i=1,2,\cdots ,N$, do the following:
  Choose [Lpi​​:Rpi​​] 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:

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