P17196 [KOI 2026 #2] Sequence Operations

You are given a sequence $A=[A_1,A_2,\cdots,A_N]$ of length $N$ and a sequence $B=[B_1,B_2,\cdots,B_M]$ of length $M$. Sequence $A$ is a sequence formed by each of the integers $1,2,\cdots,N$ appearing exactly once. Each element of sequence $B$ is between $1$ and $N$, and all elements are pairwise distinct. Let the sequence to be operated on be $X$. Initially, sequence $X$ is the same as sequence $A$. You may perform the following two operations on $X$ any number of times (possibly zero times). - **Swap operation** Let $X=[X_1,X_2,\cdots,X_K]$. Choose an integer $i$ such that $1 \le i \le K-1$ and $X_i

The first line contains two integers $N$ and $M$ separated by spaces. The second line contains $N$ integers $A_1,A_2,\cdots,A_N$ separated by spaces. The third line contains $M$ integers $B_1,B_2,\cdots,B_M$ separated by spaces.

If it is impossible to transform sequence $X$ into sequence $B$, output `NO` on the first line. If it is possible to transform sequence $X$ into sequence $B$, output in the following format. Output `YES` on the first line. Output the number of operations $Q$ on the second line. $Q$ must satisfy: $0 \le Q \le N^2$ In the next $Q$ lines, output each operation in the order performed. Each operation must use one of the following two formats. - `1 i` Perform the swap operation on the $i$-th and $(i+1)$-th elements of sequence $X$. Let the length of sequence $X$ before this operation be $K$. Then it must satisfy $1 \le i \le K-1$, and the value of the $i$-th element of sequence $X$ must be less than the value of the $(i+1)$-th element. - `2 i` Perform the merge operation on the $i$-th and $(i+1)$-th elements of sequence $X$. Let the length of sequence $X$ before this operation be $K$. Then it must satisfy $1 \le i \le K-1$. All positions are based on sequence $X$ before performing the corresponding operation, and the first position in the sequence is numbered $1$. After executing all operations in the given output in order, the resulting sequence must be exactly the same as sequence $B$. If multiple valid outputs exist, any one of them is accepted. If sequence $X$ can be transformed into sequence $B$ using the given operations, it can be proven that there always exists an output satisfying all the conditions above.

### Sample 1 Explanation Sequence $X$ changes as follows: $[1,4,2,3]\to[4,1,2,3]\to[4,2,1,3]\to[4,2,3,1]\to[2,3,1]\to[3,2,1]\to[3,1]$ Therefore, sequence $X$ can be transformed into sequence $B$. ### Constraints - All given numbers are integers. - $1 \le M \le N \le 3\,000$ - Sequence $A$ is a permutation of $1,2,\cdots,N$, i.e. $\{A_1,A_2,\cdots,A_N\}=\{1,2,\cdots,N\}$. - For each integer $i$ ($1 \le i \le M$), $1 \le B_i \le N$. - $B_1,B_2,\cdots,B_M$ are pairwise distinct. ### Subtasks 1. ($7$ points) $N \le 8$. 2. ($8$ points) $M=1$. 3. ($12$ points) $M=N$. 4. ($10$ points) For each integer $i$ ($1 \le i \le N$), $A_i=i$. 5. ($13$ points) $M=N-1$. 6. ($15$ points) Sequence $B$ is a subsequence of sequence $A$. In other words, there exist integers $p_1,p_2,\cdots,p_M$ satisfying $1 \le p_1