Problem:
Score : 600 points

Problem Statement

We have a rectangular grid of squares with H horizontal rows and W vertical columns. Let (i,j) denote the square at the i-th row from the top and the j-th column from the left.
On this grid, there is a piece, which is initially placed at square (s_r,s_c).

Takahashi and Aoki will play a game, where each player has a string of length N.
Takahashi's string is S, and Aoki's string is T. S and T both consist of four kinds of letters: L, R, U and D.

The game consists of N steps. The i-th step proceeds as follows:

First, Takahashi performs a move. He either moves the piece in the direction of S_i, or does not move the piece.

Second, Aoki performs a move. He either moves the piece in the direction of T_i, or does not move the piece.

Here, to move the piece in the direction of L, R, U and D, is to move the piece from square (r,c) to square (r,c-1), (r,c+1), (r-1,c) and (r+1,c), respectively. If the destination square does not exist, the piece is removed from the grid, and the game ends, even if less than N steps are done.

Takahashi wants to remove the piece from the grid in one of the N steps.
Aoki, on the other hand, wants to finish the N steps with the piece remaining on the grid.
Determine if the piece will remain on the grid at the end of the game when both players play optimally.

Constraints

2 \leq H,W \leq 2 \times 10^5

2 \leq N \leq 2 \times 10^5

1 \leq s_r \leq H

1 \leq s_c \leq W

|S|=|T|=N

S and T consists of the four kinds of letters L, R, U and D.

Input

Input is given from Standard Input in the following format:

H W N
s_r s_c
S
T

Output

If the piece will remain on the grid at the end of the game, print YES; otherwise, print NO.

Sample Input 1

2 3 3
2 2
RRL
LUD

Sample Output 1

YES

Here is one possible progress of the game:

Takahashi moves the piece right. The piece is now at (2,3).

Aoki moves the piece left. The piece is now at (2,2).

Takahashi does not move the piece. The piece remains at (2,2).

Aoki moves the piece up. The piece is now at (1,2).

Takahashi moves the piece left. The piece is now at (1,1).

Aoki does not move the piece. The piece remains at (1,1).

Sample Input 2

4 3 5
2 2
UDRRR
LLDUD

Sample Output 2

NO

Sample Input 3

5 6 11
2 1
RLDRRUDDLRL
URRDRLLDLRD

Sample Output 3

NO

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

using ll=long long;
#define rng(i,l,r) for(int i=int(l);i<int(r);i++)
#define rep(i,r) rng(i,0,r)
#define rrng(i,l,r) for(int i=int(r)-1;i>=int(l);i--)
#define rrep(i,r) rrng(i,0,r)
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define F first
#define S second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#define inf INT_MAX/2-100
#define infl LLONG_MAX/3
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<' '<<#x<<' '<<x<<endl
#else
#define dmp(x) void(0)
#endif
 
template<class t,class u>bool chmax(t&a,u b){if(a<b)a=b;return a<b;}
template<class t,class u>bool chmin(t&a,u b){if(b<a)a=b;return b<a;}
 
template<class t>using vc=vector<t>;
template<class t>using vvc=vector<vector<t>>;
 
using pi=pair<int,int>;
using pl=pair<ll,ll>;
using vi=vc<int>;
using vl=vc<ll>;
 
 
ll readl(void){
	ll x;
	cin>>x;
	return x;
}
int readi(void){
	int x;
	cin>>x;
	return x;
}
 
string readstr(){
	string s;
	cin>>s;
	return s;
}
vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=readi(),v[i]+=off;
	return v;
}
 
vl readvl(int n,int off=0){
	vl v(n);
	rep(i,n)v[i]=readl(),v[i]+=off;
	return v;
}
 
template<class t>
void print(t x,int suc=1){
	cout<<x;
	if(suc==1)cout<<"\n";
	if(suc==2)cout<<" ";
}
 
template<class t>
void print(const vc<t>&v,int suc=1){
	rep(i,si(v))print(v[i],i==int(si(v))-1?1:suc);
}
 
template<class t>
bool inc(t a,t b,t c){
	return !(c<b||b<a);
}
 
template<class t>
void compress(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}
 
template<class t>
int lwb(const vc<t>&v,const t&a){
	return lower_bound(all(v),a)-v.bg;
}
 
template<class t>
struct Compress{
	vc<t>v;
	Compress()=default;
	Compress(const vc<t>&x){
		add(x);
	}
	Compress(const initializer_list<vc<t> >&x){
		for(auto &p:x)add(p);
	}
	void add(const t&x){
		v.eb(x);
	}
	void add(const vc<t>&x){
		copy(all(x),back_inserter(v));
	}
	void build(){
		compress(v);
	}
	int get(const t&x)const{
		return lwb(v,x);
	}
	vc<t>get(const vc<t>&x)const{
		vc<t>res(x);
		for(auto &p:res)p=get(p);
		return res;
	}
	const t &operator[](int x)const{
		return v[x];
	}
};
void Yes(bool ex=true){
	cout<<"Yes\n";
	if(ex)exit(0);
}
void YES(bool ex=true){
	cout<<"YES\n";
	if(ex)exit(0);
}
void No(bool ex=true){
	cout<<"No\n";
	if(ex)exit(0);
}
void NO(bool ex=true){
	cout<<"NO\n";
	if(ex)exit(0);
}
void orYes(bool x,bool ex=true){
	if(x)Yes(ex);
	else No(ex);
}
void orYES(bool x,bool ex=true){
	if(x)YES(ex);
	else NO(ex);
}
void Possible(bool ex=true){
	cout<<"Possible\n";
	if(ex)exit(0);
}
void POSSIBLE(bool ex=true){
	cout<<"POSSIBLE\n";
	if(ex)exit(0);
}
void Impossible(bool ex=true){
	cout<<"Impossible\n";
	if(ex)exit(0);
}
void IMPOSSIBLE(bool ex=true){
	cout<<"IMPOSSIBLE\n";
	if(ex)exit(0);
}
void orPossible(bool x,bool ex=true){
	if(x)Possible(ex);
	else Impossible(ex);
}
void orPOSSIBLE(bool x,bool ex=true){
	if(x)POSSIBLE(ex);
	else IMPOSSIBLE(ex);
}
int main(void){
	cin.tie(0);
	ios::sync_with_stdio(0);
	int h=readi(),w=readi(),n=readi(),sy=readi(),sx=readi();
	int xmi=1,xma=w,ymi=1,yma=w;
	string s=readstr(),t=readstr();
	for(int i=n-1;i>=0;i--){
		if(t[i]=='R')xmi=max(1,xmi-1);
		if(t[i]=='L')xma=min(w,xma+1);
		if(t[i]=='D')ymi=max(1,ymi-1);
		if(t[i]=='U')yma=min(h,yma+1);

		if(s[i]=='R')xma--;
		if(s[i]=='L')xmi++;
		if(s[i]=='D')yma--;
		if(s[i]=='U')ymi++;
		if(xmi>xma||ymi>yma)NO();
	}
	orYES(xmi<=sx&&sx<=xma&&ymi<=sy&&sy<=yma);
}