One Number Hint

A and B want to get into a locked research laboratory. The entrance runs a security system that asks one question. The question is written as an integer $q$ with $1 \le q \le N$, and it must be answered with either yes or no. A correct answer opens the door, and a wrong answer sets off the alarm.

Both of them know that $q$ is always either $x$ or $y$, where $x \ne y$, the correct answer to $x$ is yes, and the correct answer to $y$ is no.

While they were planning, neither could recall the actual values of $x$ and $y$. So B walks up to the entrance alone and A waits far away. The moment the question appears, A remembers $x$ and $y$. From that distance A cannot explain anything to B. A can only shout one integer $h$. Everything B needs has to fit into that single $h$.

Write a program that plays both parts. In the first run it reads $N$, $x$, $y$ and prints the number $h$ that A shouts. In the second run it reads $N$, $q$, $h$ and prints the answer B should give.

The two runs are judged separately, so the rule that turns $(x, y)$ into $h$ and the rule that turns $(q, h)$ into an answer are both fixed here.

The subset table. Take every 6-element subset of $\{1, 2, \dots, 12\}$, write each subset as its elements in increasing order, and sort those sequences lexicographically. There are 924 such subsets. Let $S(v)$ be the $v$-th subset in this order, counting from 1. The first four are $S(1) = \{1,2,3,4,5,6\}$, $S(2) = \{1,2,3,4,5,7\}$, $S(3) = \{1,2,3,4,5,8\}$ and $S(4) = \{1,2,3,4,5,9\}$, and the last one is $S(924) = \{7,8,9,10,11,12\}$.

The number A shouts. For a pair $(x, y)$, $h$ is the smallest number that belongs to $S(x)$ and not to $S(y)$. Two different subsets of the same size never contain one another, so such a number always exists.

The answer B gives. For a pair $(q, h)$, the answer is yes if $h \in S(q)$, and no otherwise.

The first line contains a single integer, either 1 or 2.

If it is 1, the program plays A. The second line contains $N$ and $T$. The $i$-th of the next $T$ lines contains $x$ and $y$ ($1 \le x, y \le N$, $x \ne y$).

If it is 2, the program plays B. The second line contains $N$ and $T$. The $i$-th of the next $T$ lines contains $q$ and $h$ ($1 \le q \le N$, $1 \le h \le 12$).

If the program plays A, print $T$ lines. The $i$-th line holds the number $h$ for test case $i$, computed by the rule above.

If the program plays B, print $T$ lines. The $i$-th line holds the answer for test case $i$, computed by the rule above, written as yes or no.

In every test case $1 \le N \le 920$ and $1 \le T \le 10\,000$.