Drainage

The ChAOS country has $N$ cities, numbered $1$ through $N$. Each city has a drainage ditch that prevents flooding. The drainage ditch of city $i$ can prevent flooding only when the rainfall is at most $A_i$.

To prepare for heavy rain in a single city, the country decides to build a project that pools the drainage capacity of two cities. For example, after building the project on cities $1$ and $2$, if the sum of the rainfall of cities $1$ and $2$ is at most $A_1 + A_2$, both cities 1 and 2 are protected from flooding. Otherwise, both cities flood. If the project is then built on cities $2$ and $3$ as well, and the sum of the rainfall of cities $1$, $2$, and $3$ is at most $A_1 + A_2 + A_3$, all three cities are protected. Otherwise, all three cities flood.

Heavy rain is now falling across the country. The current rainfall of city $i$ is $B_i$. Write a program that processes two kinds of queries.

• $1$ $x$ $y$: Build the project on city $x$ and city $y$.
• $2$: Print the number of cities that flood in the current state.

There is at least one query of type $2$.

The first line contains the number of cities $N$ ($3 \le N \le 100000$) and the number of queries $M$ ($1 \le M \le 100000$).

The second line contains $N$ integers $A_1, A_2, \ldots, A_N$ ($0 \le A_i \le 1000$).

The third line contains $N$ integers $B_1, B_2, \ldots, B_N$ ($0 \le B_i \le 1000$).

From the fourth line through line $M + 3$, each line contains one query in the form $1$ $x$ $y$ or $2$ ($1 \le x, y \le N$).

For each query of type $2$, print the answer on its own line.