Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import math
import bisect
Q = int(input())
for _ in range(Q):
    A, B, C, D = map(int, input().split())
    K = math.ceil(max(A, B) / (min(A, B) + 1))
    xs = ((A - i + 1) * K < B - max(0, (i - 1) // K) for i in range(A + 1))
    p = bisect.bisect(list(xs), False)
    f = ''
    for i in range(C - 1, D):
        na = p - 1
        nb = max(0, (na - 1) // K)
        if i < nb * (K + 1):
            f += ('A', 'B')[i % (K + 1) == K]
        elif i < na + nb:
            f += 'A'
        else:
            j = A + B - i - 1
            nb = B - nb
            na = max(0, (nb - 1) // K)
            if j < na * (K + 1):
                f += ('B', 'A')[j % (K + 1) == K]
            else:
                f += 'B'
    print(f)


Fixed submission:
#!/usr/bin/env python3
import math
Q = int(input())
for _ in range(Q):
    A, B, C, D = map(int, input().split())
    K = math.ceil(max(A, B) / (min(A, B) + 1))
    lo, hi = 0, A + 1
    while hi - lo > 1:
        mid = (lo + hi) // 2
        rA, rB = A - mid, B - max(0, (mid - 1) // K)
        if (rA + 1) * K < rB:
            hi = mid
        else:
            lo = mid

    f = ''
    for i in range(C - 1, D):
        na = lo
        nb = max(0, (na - 1) // K)
        if i < nb * (K + 1):
            f += ('A', 'B')[i % (K + 1) == K]
        elif i < na + nb:
            f += 'A'
        else:
            j = A + B - i - 1
            nb = B - nb
            na = max(0, (nb - 1) // K)
            if j < na * (K + 1):
                f += ('B', 'A')[j % (K + 1) == K]
            else:
                f += 'B'
    print(f)

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import math
Q = int(input())
for _ in range(Q):
    A, B, C, D = map(int, input().split())
    K = math.ceil(max(A, B) / (min(A, B) + 1))
    f = ''
    ca, cb = 0, 0
    while A + B > 0:
        if B <= A * K:
            if A > 0 and ca < K:
                A -= 1
                ca += 1
                cb = 0
                f += 'A'
            elif B > 0:
                B -= 1
                ca = 0
                cb += 1
                f += 'B'
        else:
            if B > 0 and cb < K:
                B -= 1
                ca = 0
                cb += 1
                f += 'B'
            elif A > 0:
                A -= 1
                ca += 1
                cb = 0
                f += 'A'
    print(f[C - 1:D])


Fixed submission:
#!/usr/bin/env python3
import math
Q = int(input())
for _ in range(Q):
    A, B, C, D = map(int, input().split())
    K = math.ceil(max(A, B) / (min(A, B) + 1))
    lo, hi = 0, A + 1
    while hi - lo > 1:
        mid = (lo + hi) // 2
        rA, rB = A - mid, B - max(0, (mid - 1) // K)
        if (rA + 1) * K < rB:
            hi = mid
        else:
            lo = mid

    f = ''
    for i in range(C - 1, D):
        na = lo
        nb = max(0, (na - 1) // K)
        if i < nb * (K + 1):
            f += ('A', 'B')[i % (K + 1) == K]
        elif i < na + nb:
            f += 'A'
        else:
            j = A + B - i - 1
            nb = B - nb
            na = max(0, (nb - 1) // K)
            if j < na * (K + 1):
                f += ('B', 'A')[j % (K + 1) == K]
            else:
                f += 'B'
    print(f)