A16291. Robot Queries

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 $s_1 s_2 s_3 \dots s_{l-1} s_r s_{r-1} s_{r-2} \dots s_l s_{r+1} s_{r+2} \dots s_n$ ).

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.

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.

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: