The Game

There is a legend that in the 18th century mathematicians enjoyed the following game.

Three mathematicians take part, and one of them is the game master. The game master first announces a positive integer $N$. He then secretly chooses two different integers $X$ and $Y$, each between $1$ and $N$ inclusive, and privately tells their sum $X + Y$ to player $S$ and their product $X \cdot Y$ to player $P$. Each player learns only their own value and knows whether it is the sum or the product.

The two players then speak in turns, always in the fixed order $S$, $P$, $S$, $P$, $\dots$ — player $S$ always speaks first. On each turn the current player announces either "I know these numbers" or "I don't know these numbers", reasoning only from their own value and from every statement made so far (all statements are public). A player can name the pair exactly when only one pair is still consistent with everything known. The game ends the instant a player says "I know".

For example, the dialog might go like this:

• Game master: "Let $N$ be $10$." (then he chooses two numbers from $1$ to $10$ and tells their sum to $S$ and their product to $P$)
• Player $S$: "I don't know these numbers."
• Player $P$: "I don't know these numbers."
• Player $S$: "I don't know these numbers."
• Player $P$: "I don't know these numbers."
• Player $S$: "Now I know these numbers — you chose $3$ and $6$."

You are given $N$ and $M$, where $M$ is the total number of times "I don't know these numbers" was said before the game ended (so the final "I know" is statement number $M + 1$). Find every pair of numbers the game master could have chosen.

One line with two integers $N$ and $M$ ($2 \le N \le 200$, $0 \le M \le 100$).

On the first line, print the number of pairs the game master could have chosen from $1$ to $N$ so that the players said "I don't know these numbers" exactly $M$ times before someone said "I know".

Then print those pairs, one per line, each as two integers "$a$ $b$" with $a < b$. Print the pairs in ascending order: sorted by the first number, and by the second number when the first numbers are equal.