Robot Queries
Description
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.
Input
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
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.
8 3
RDLLUURU
-1 2 1 7
0 0 3 4
0 1 7 8
4 2
RLDU
0 0 2 2
-1 -1 2 3
10 6
DLUDLRULLD
-1 0 1 10
-1 -2 2 5
-4 -2 6 10
-1 0 3 9
0 1 4 7
-3 -1 5 8
YES
YES
NO
YES
NO
YES
YES
YES
NO
YES
YES
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:
