Buggy python submission (verdict: Time Limit Exceeded):
from operator import add


class SegTree():
    def __init__(self, N, e, operator_func=add):
        self.e = e # 単位元
        self.size = N
        self.node = [self.e] * (2*N)
        self.operator_func = operator_func # 処理(add or xor max minなど)

    def set_list(self, l):
        for i in range(self.size):
            self.node[i+self.size-1] = l[i]
        for i in range(self.size-1)[::-1]:
            self.node[i] = self.operator_func(self.node[2*i+1], self.node[2*i+2])
    
    def update(self, k, x):
        k += self.size-1
        self.node[k] = x
        while k >= 0:
            k = (k - 1) // 2
            self.node[k] = self.operator_func(self.node[2*k+1], self.node[2*k+2])

    def get(self, l, r):
        # [l, r) についてqueryを求める
        x = self.e
        l += self.size
        r += self.size

        while l<r:
            if l&1:
                x = self.operator_func(x, self.node[l-1])
                l += 1
            if r&1:
                r -= 1
                x = self.operator_func(x, self.node[r-1])
            l >>= 1
            r >>= 1
        return x


S = input()
T = input()
treeS = SegTree(len(S), 0)
treeT = SegTree(len(T), 0)
treeS.set_list([1 if s=="A" else 0 for s in S])
treeT.set_list([1 if s=="A" else 0 for s in T])

q = int(input())
for _ in range(q):
    a, b, c, d = map(int, input().split())
    sa = treeS.get(a-1, b)
    sb = b-a+1-sa
    ta = treeT.get(c-1, d)
    tb = d-c+1-ta

    if (2*(sb-sa)+tb-ta)%3 or (sb-sa+2*(tb-ta))%3:
        print("NO")
    else:
        print("YES")



Fixed submission:
from operator import add
import sys
input=sys.stdin.readline


class SegTree():
    def __init__(self, N, e, operator_func=add):
        self.e = e # 単位元
        self.size = N
        self.node = [self.e] * (2*N)
        self.operator_func = operator_func # 処理(add or xor max minなど)

    def set_list(self, l):
        for i in range(self.size):
            self.node[i+self.size-1] = l[i]
        for i in range(self.size-1)[::-1]:
            self.node[i] = self.operator_func(self.node[2*i+1], self.node[2*i+2])
    
    def update(self, k, x):
        k += self.size-1
        self.node[k] = x
        while k >= 0:
            k = (k - 1) // 2
            self.node[k] = self.operator_func(self.node[2*k+1], self.node[2*k+2])

    def get(self, l, r):
        # [l, r) についてqueryを求める
        x = self.e
        l += self.size
        r += self.size

        while l<r:
            if l&1:
                x = self.operator_func(x, self.node[l-1])
                l += 1
            if r&1:
                r -= 1
                x = self.operator_func(x, self.node[r-1])
            l >>= 1
            r >>= 1
        return x


def main():
    S = input()
    T = input()
    treeS = SegTree(len(S), 0)
    treeT = SegTree(len(T), 0)
    treeS.set_list([1 if s=="A" else 0 for s in S])
    treeT.set_list([1 if s=="A" else 0 for s in T])

    q = int(input())
    for _ in range(q):
        a, b, c, d = map(int, input().split())
        sa = treeS.get(a-1, b)
        sb = b-a+1-sa
        ta = treeT.get(c-1, d)
        tb = d-c+1-ta

        if (2*(sb-sa)+tb-ta)%3 or (sb-sa+2*(tb-ta))%3:
            print("NO")
        else:
            print("YES")

main()