Problem:
Score : 600 points

Problem Statement

Let us consider the following operations on a string consisting of A and B:

Select a character in a string. If it is A, replace it with BB. If it is B, replace with AA.

Select a substring that is equal to either AAA or BBB, and delete it from the string.

For example, if the first operation is performed on ABA and the first character is selected, the string becomes BBBA.
If the second operation is performed on BBBAAAA and the fourth through sixth characters are selected, the string becomes BBBA.

These operations can be performed any number of times, in any order.

You are given two string S and T, and q queries a_i, b_i, c_i, d_i.
For each query, determine whether S_{a_i} S_{{a_i}+1} ... S_{b_i}, a substring of S, can be made into T_{c_i} T_{{c_i}+1} ... T_{d_i}, a substring of T.

Constraints

1 \leq |S|, |T| \leq 10^5

S and T consist of letters A and B.

1 \leq q \leq 10^5

1 \leq a_i \leq b_i \leq |S|

1 \leq c_i \leq d_i \leq |T|

Input

Input is given from Standard Input in the following format:

S
T
q
a_1 b_1 c_1 d_1
...
a_q b_q c_q d_q

Output

Print q lines. The i-th line should contain the response to the i-th query. If S_{a_i} S_{{a_i}+1} ... S_{b_i} can be made into T_{c_i} T_{{c_i}+1} ... T_{d_i}, print YES. Otherwise, print NO.

Sample Input 1

BBBAAAABA
BBBBA
4
7 9 2 5
7 9 1 4
1 7 2 5
1 7 2 4

Sample Output 1

YES
NO
YES
NO

The first query asks whether the string ABA can be made into BBBA.
As explained in the problem statement, it can be done by the first operation.

The second query asks whether ABA can be made into BBBB, and the fourth query asks whether BBBAAAA can be made into BBB.
Neither is possible.

The third query asks whether the string BBBAAAA can be made into BBBA.
As explained in the problem statement, it can be done by the second operation.

Sample Input 2

AAAAABBBBAAABBBBAAAA
BBBBAAABBBBBBAAAAABB
10
2 15 2 13
2 13 6 16
1 13 2 20
4 20 3 20
1 18 9 19
2 14 1 11
3 20 3 15
6 16 1 17
4 18 8 20
7 20 3 14

Sample Output 2

YES
YES
YES
YES
YES
YES
NO
NO
NO
NO

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
//using System.Numerics;  //comment out if AOJ
using System.Text;

using Problem = Tmp.Problem;
using MyIO;

#pragma warning disable   //for AOJ

namespace Tmp
{
    class Problem : IDisposable
    {
        bool IsGCJ;
        int Repeat;
        Scanner sc;
        Printer pr;
        public Problem(bool isGCJ, Scanner scanner, Printer printer)
        {
            sc = scanner;
            pr = printer;
            IsGCJ = isGCJ;
            if (isGCJ) Repeat = sc.nextInt();
            else Read();
        }
        public Problem(bool isGCJ) : this(isGCJ, new Scanner(), new Printer()) { }
        public Problem(bool isGCJ, Scanner scanner) : this(isGCJ, scanner, new Printer()) { }
        public Problem(bool isGCJ, Printer printer) : this(isGCJ, new Scanner(), printer) { }
        public void Solve()
        {
            if (IsGCJ) for (var i = 0; i < Repeat; i++) { Read(); pr.Write("Case #" + (i + 1) + ": "); SolveOne(); }
            else SolveOne();
        }
        public void Dispose()
        {
            sc.Dispose();
            pr.Dispose();
        }
        public int Size { get { return 1; } }
        public const long Mod = 1000000007;

        // 使用する変数をここに書く
        // string S;
        // int a;
        /// <summary>
        /// 読み込み処理をここに書く
        /// </summary>
        void Read()
        {

        }
        /// <summary>
        /// メイン処理をここに書く
        /// </summary>
        void SolveOne()
        {
            string s = sc.next();
            string t = sc.next();
            int q = sc.nextInt();
            int[] sa = new int[s.Length + 1];
            int[] sb = new int[s.Length + 1];
            int[] ta = new int[t.Length + 1];
            int[] tb = new int[t.Length + 1];
            for (int i = 0; i < s.Length; i++)
            {
                sa[i + 1] = sa[i];
                sb[i + 1] = sb[i];
                if (s[i] == 'A') sa[i + 1]++;
                else sb[i + 1]++;
            }
            for (int i = 0; i < t.Length; i++)
            {
                ta[i + 1] = ta[i];
                tb[i + 1] = tb[i];
                if (t[i] == 'A') ta[i + 1]++;
                else tb[i + 1]++;
            }
            for (int qq = 0; qq < q; qq++)
            {
                int a = sc.nextInt();
                int b = sc.nextInt();
                int c = sc.nextInt();
                int d = sc.nextInt();
                int aBef = (sa[b] - sa[a - 1]) % 3;
                int bBef = (sb[b] - sb[a - 1]) % 3;
                int aAft = (ta[d] - ta[c - 1]) % 3;
                int bAft = (tb[d] - tb[c - 1]) % 3;

                pr.WriteLine(Judge(aBef, bBef) == Judge(aAft, bAft));
                //if (Judge(aBef, bBef) == Judge(aAft, bAft)) Console.WriteLine("YES");
                //else Console.WriteLine("NO");
            }

        }
        int Judge(int a, int b)
        {
            if ((a == 1 && b == 0) || (a == 0 && b == 2) || (a == 2 && b == 1)) return 0;    //from A
            if ((a == 0 && b == 1) || (a == 2 && b == 0) || (a == 1 && b == 2)) return 1;    //from B
            return 2;   // from AB
        }
    }
}
class Program
{
    //public static RandomSFMT rand = new RandomSFMT();
    public static bool IsJudgeMode = true;
    public static bool IsGCJMode = false;
    public static bool IsSolveCreated = true;
    static void Main()
    {
        if (IsJudgeMode)
            if (IsGCJMode) using (var problem = new Problem(true, new Scanner("C-large-practice.in.txt"), new Printer("output.txt"))) problem.Solve();
            else using (var problem = new Problem(false, new Printer())) problem.Solve();
        else
        {
            var num = 1;
            int size = 0;
            decimal time = 0;
            for (var tmp = 0; tmp < num; tmp++)
            {
                using (var P = IsSolveCreated ? new Problem(false, new Scanner("input.txt"), new Printer()) : new Problem(false))
                {
                    size = P.Size;
                    //time += Func.MeasureTime(() => P.Solve());
                }
            }
            Console.WriteLine("{0}, {1}ms", size, time / num);
        }
    }
}

/// <summary>
/// カスタマイズしたIO
/// </summary>
namespace MyIO
{
    class Printer : IDisposable
    {
        bool isConsole;
        TextWriter file;
        public Printer() { file = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; isConsole = true; }
        public Printer(string path) { file = new StreamWriter(path, false) { AutoFlush = false }; isConsole = false; }
        public void Write<T>(T value) { file.Write(value); }
        public void Write(bool b) { file.Write(b ? "YES" : "NO"); }
        public void Write(string str, params object[] args) { file.Write(str, args); }
        public void WriteLine() { file.WriteLine(); }
        public void WriteLine<T>(T value) { file.WriteLine(value); }
        public void WriteLine(bool b) { file.WriteLine(b ? "YES" : "NO"); }
        public void WriteLine<T>(IEnumerable<T> list) { foreach (var x in list) file.WriteLine(x); }
        public void WriteLine<T>(List<T> list) { foreach (var x in list) file.WriteLine(x); }
        public void WriteLine<T>(T[] list) { foreach (var x in list) file.WriteLine(x); }
        public void WriteLine(string str, params object[] args) { file.WriteLine(str, args); }
        public void Dispose() { file.Flush(); if (!isConsole) file.Dispose(); }
    }
    class Scanner : IDisposable
    {
        bool isConsole;
        TextReader file;
        public Scanner() { file = Console.In; }
        public Scanner(string path) { file = new StreamReader(path); isConsole = false; }
        public void Dispose() { if (!isConsole) file.Dispose(); }

        #region next読み込み
        string[] nextBuffer = new string[0];
        int BufferCnt = 0;

        char[] cs = new char[] { ' ' };

        public string next()
        {
            while (BufferCnt >= nextBuffer.Length)
            {
                string st = file.ReadLine();
                while (st == "") st = file.ReadLine();
                nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
                BufferCnt = 0;
            }
            return nextBuffer[BufferCnt++];
        }

        public int nextInt()
        {
            return int.Parse(next());
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }

        private T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public string[] next(int n) { return enumerate(n, next); }
        public double[] nextDouble(int n) { return enumerate(n, nextDouble); }
        public int[] nextInt(int n) { return enumerate(n, nextInt); }
        public long[] nextLong(int n) { return enumerate(n, nextLong); }
        #endregion
    }
}