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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class Program
{
    static int H, W, N;
    static int sr, sc;
    static string S,T;

    static int rD, rU, rR, rL;

    public static void Main(string[] args)
    {
        H = Input.NextInt();
        W = Input.NextInt();
        N = Input.NextInt();
        sr = Input.NextInt() - 1;
        sc = Input.NextInt() - 1;
        S = Input.NextString();
        T = Input.NextString();


         rD = H - sr;
         rU = sr + 1;
         rR = sc + 1;
         rL = W - sc;

        for (int i = 1; i < N; i++)
        {
            bool isNo = NewMethod(N);
            if (isNo)
            {
                Console.WriteLine("NO");
                return;
            }
        }

        Console.WriteLine("YES");
    }


    private static bool NewMethod(int nn)
    {
        bool isNo = false;

        var sss = S.Substring(0, nn);
        var ttt = T.Substring(0, nn);
        var cSU = sss.Count(n => n == 'U');
        var cTU = ttt.Count(n => n == 'U');
        var cSD = sss.Count(n => n == 'D');
        var cTD = ttt.Count(n => n == 'D');
        var cSR = sss.Count(n => n == 'R');
        var cTR = ttt.Count(n => n == 'R');
        var cSL = sss.Count(n => n == 'L');
        var cTL = ttt.Count(n => n == 'L');



        bool SgoD = rD <= cSD;
        bool SgoU = rU <= cSU;
        bool SgoR = rR <= cSR;
        bool SgoL = rR <= cSL;

        if (SgoU)
        {
            var r = sr;
            for (int i = 0; i < nn; i++)
            {
                if (S[i] == 'U')
                {
                    r--;
                    if (r < 0)
                    {
                        isNo = true;
                        goto L100;
                    }
                }
                if (T[i] == 'D' && r < H - 1)
                {
                    r++;
                }
            }
        }

        if (SgoD)
        {
            var r = sr;
            for (int i = 0; i < nn; i++)
            {
                if (S[i] == 'D')
                {
                    r++;
                    if (r >= H)
                    {
                        isNo = true;
                        goto L100;
                    }
                }
                if (T[i] == 'U' && r > 0)
                {
                    r--;
                }
            }
        }

        if (SgoR)
        {
            var r = sr;
            for (int i = 0; i < nn; i++)
            {
                if (S[i] == 'R')
                {
                    r--;
                    if (r < 0)
                    {
                        isNo = true;
                        goto L100;

                    }
                }
                if (T[i] == 'L' && r < W - 1)
                {
                    r++;
                }
            }
        }

        if (SgoL)
        {
            var r = sr;
            for (int i = 0; i < nn; i++)
            {
                if (S[i] == 'L')
                {
                    r++;
                    if (r >= W)
                    {
                        isNo = true;
                        goto L100;

                    }
                }
                if (T[i] == 'R' && r > 0)
                {
                    r--;
                }
            }
        }
    L100:
        ;
        return isNo;
    }
}

public static class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}