1902D · Robot Queries

Problem: There is an infinite $2$-dimensional grid. Initially, a robot stands in the point $(0, 0)$. The robot can execute four commands:

• U — move from point $(x, y)$ to $(x, y + 1)$;
• D — move from point $(x, y)$ to $(x, y - 1)$;
• L — move from point $(x, y)$ to $(x - 1, y)$;
• R — move from point $(x, y)$ to $(x + 1, y)$.

You are given a sequence of commands $s$ of length $n$. Your task is to answer $q$ independent queries: given four integers $x$, $y$, $l$ and $r$; determine whether the robot visits the point $(x, y)$, while executing a sequence $s$, but the substring from $l$ to $r$ is reversed (i. e. the robot performs commands in order $s_1 s_2 s_3 \dots s_{l-1} s_r s_{r-1} s_{r-2} \dots s_l s_{r+1} s_{r+2} \dots s_n$).

Input Format: The first line contains two integers $n$ and $q$ ($1 \le n, q \le 2 \cdot 10^5$) — the length of the command sequence and the number of queries, respectively.

The second line contains a string $s$ of length $n$, consisting of characters U, D, L and/or R.

Then $q$ lines follow, the $i$-th of them contains four integers $x_i$, $y_i$, $l_i$ and $r_i$ ($-n \le x_i, y_i \le n$; $1 \le l \le r \le n$) describing the $i$-th query.

Output Format: For each query, print YES if the robot visits the point $(x, y)$, while executing a sequence $s$, but the substring from $l$ to $r$ is reversed; otherwise print NO.

Note: In the first query of the first sample, the path of the robot looks as follows:

In the second query of the first sample, the path of the robot looks as follows:

In the third query of the first sample, the path of the robot looks as follows: