Obstacles for a Llama

A llama wants to travel through the Andean Plateau. It has a map of the plateau in the form of a grid of $N \times M$ square cells. The rows of the map are numbered from $0$ to $N-1$ from top to bottom, and the columns are numbered from $0$ to $M-1$ from left to right. The cell of the map in row $i$ and column $j$ ($0 \leq i < N, 0 \leq j < M$) is denoted by $(i, j)$.

The llama has studied the climate of the plateau and discovered that all cells in each row of the map have the same temperatureand all cells in each column of the map have the same humidity. The llama has given you two integer arrays $T$ and $H$ of length $N$ and $M$ respectively. Here $T\[i]$ ($0 \leq i < N$) indicates the temperature of the cells in row $i$, and $H\[j]$ ($0 \leq j < M$) indicates the humidity of the cells in column $j$.

The llama has also studied the flora of the plateau and noticed that a cell $(i, j)$ is free of vegetation if and only if its temperature is greater than its humidity, formally $T\[i] > H\[j]$.

The llama can travel across the plateau only by following valid paths. A valid path is a sequence of distinct cells that satisfy the following conditions:

• Each pair of consecutive cells in the path shares a common side.
• All cells in the path are free of vegetation.

Your task is to answer $Q$ questions. For each question, you are given four integers: $L, R, S$, and $D$. You must determine whether there exists a valid path such that:

• The path starts at cell $(0, S)$ and ends at cell $(0, D)$.
• All cells in the path lie within columns $L$ to $R$, inclusive.

It is guaranteed that both $(0, S)$ and $(0, D)$ are free of vegetation.

• $1 \leq N, M, Q \leq 200\\,000$
• $0 \leq T\[i] \leq 109$ for each $i$ such that $0 \leq i < N$.
• $0 \leq H\[j] \leq 109$ for each $j$ such that $0 \leq j < M$.
• $0 \leq L \leq R < M$
• $L \leq S \leq R$
• $L \leq D \leq R$
• Both cells $(0, S)$ and $(0, D)$ are free of vegetation.