Buggy python submission (verdict: Runtime Error):
# def C(n, r ,mod=10**9+7):
#     if n-r<r: r=n-r
#     if r == 0: return 1
#     if r == 1: return n
# 
#     numerator = [n - r + k + 1 for k in range(r)]
#     denominator = [k + 1 for k in range(r)]
# 
#     for p in range(2,r+1):
#         pivot = denominator[p - 1]
#         if pivot > 1:
#             offset = (n - r) % p
#             for k in range(p-1,r,p):
#                 numerator[k - offset] /= pivot
#                 denominator[k] /= pivot
# 
#     result = 1
#     for k in range(r):
#         if numerator[k] > 1:
#             result *= int(numerator[k]) %mod
# 
#     return result % mod

A=list(input())
n=len(A)
mod=10**9+7
ans=0
numa= A[0]=="A" 
numa_= A[0]=="?"
numc=A[2:].count("C")
numc_= A[2:].count("?")

for i in range(1,n-1):
    #print(numa,numa_,numc,numc_)
    apro=cpro=0
    if A[i]=="B" or A[i]=="?":
        # for k in range(numa_+1):
        #     apro+= (((C(numa_,k)*pow(2,numa_-k,mod))%mod)*(numa+k))%mod
        # for k in range(numc_+1):
        #     cpro+= (((C(numc_,k)*pow(2,numc_-k,mod))%mod)*(numc+k))%mod
        #print(apro,cpro)
        apro= (3*numa+numa_)*3**(numa_-1)
        cpro= (3*numc+numc_)*3**(numc_-1)
        ans+= (apro*cpro)%mod
        ans%=mod
    if A[i] == "A":
        numa+=1
    if A[i]=="?":
        numa_+=1
    if A[i+1] =="C":
        numc-=1
    if A[i+1]=="?":
        numc_-=1
print(ans)


Fixed submission:
# def C(n, r ,mod=10**9+7):
#     if n-r<r: r=n-r
#     if r == 0: return 1
#     if r == 1: return n
# 
#     numerator = [n - r + k + 1 for k in range(r)]
#     denominator = [k + 1 for k in range(r)]
# 
#     for p in range(2,r+1):
#         pivot = denominator[p - 1]
#         if pivot > 1:
#             offset = (n - r) % p
#             for k in range(p-1,r,p):
#                 numerator[k - offset] /= pivot
#                 denominator[k] /= pivot
# 
#     result = 1
#     for k in range(r):
#         if numerator[k] > 1:
#             result *= int(numerator[k]) %mod
# 
#     return result % mod

A=list(input())
n=len(A)
mod=10**9+7
ans=0
numa= A[0]=="A" 
numa_= A[0]=="?"
numc=A[2:].count("C")
numc_= A[2:].count("?")

for i in range(1,n-1):
    #print(numa,numa_,numc,numc_)
    apro=cpro=0
    if A[i]=="B" or A[i]=="?":
        # for k in range(numa_+1):
        #     apro+= (((C(numa_,k)*pow(2,numa_-k,mod))%mod)*(numa+k))%mod
        # for k in range(numc_+1):
        #     cpro+= (((C(numc_,k)*pow(2,numc_-k,mod))%mod)*(numc+k))%mod
        #print(apro,cpro)
        apro= ((3*numa+numa_)*pow(3,(numa_-1),mod))%mod
        cpro= ((3*numc+numc_)*pow(3,(numc_-1),mod))%mod
        ans+= (apro*cpro)%mod
        ans%=mod
    if A[i] == "A":
        numa+=1
    if A[i]=="?":
        numa_+=1
    if A[i+1] =="C":
        numc-=1
    if A[i+1]=="?":
        numc_-=1
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
def C(n, r ,mod=10**9+7):
    if n-r<r: r=n-r
    if r == 0: return 1
    if r == 1: return n

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k]) %mod

    return result % mod

A=list(input())
n=len(A)
mod=10**9+7
ans=0
numa= A[0]=="A" 
numa_= A[0]=="?"
numc=A[2:].count("C")
numc_= A[2:].count("?")

for i in range(1,n-1):
    #print(numa,numa_,numc,numc_)
    apro=cpro=0
    if A[i]=="B" or A[i]=="?":
        for k in range(numa_+1):
            apro+= (((C(numa_,k)*pow(2,numa_-k,mod))%mod)*(numa+k))%mod
        for k in range(numc_+1):
            cpro+= (((C(numc_,k)*pow(2,numc_-k,mod))%mod)*(numc+k))%mod
        #print(apro,cpro)
        ans+= (apro*cpro)%mod
        ans%=mod
    if A[i] == "A":
        numa+=1
    if A[i]=="?":
        numa_+=1
    if A[i+1] =="C":
        numc-=1
    if A[i+1]=="?":
        numc_-=1
print(ans)

Fixed submission:
# def C(n, r ,mod=10**9+7):
#     if n-r<r: r=n-r
#     if r == 0: return 1
#     if r == 1: return n
# 
#     numerator = [n - r + k + 1 for k in range(r)]
#     denominator = [k + 1 for k in range(r)]
# 
#     for p in range(2,r+1):
#         pivot = denominator[p - 1]
#         if pivot > 1:
#             offset = (n - r) % p
#             for k in range(p-1,r,p):
#                 numerator[k - offset] /= pivot
#                 denominator[k] /= pivot
# 
#     result = 1
#     for k in range(r):
#         if numerator[k] > 1:
#             result *= int(numerator[k]) %mod
# 
#     return result % mod

A=list(input())
n=len(A)
mod=10**9+7
ans=0
numa= A[0]=="A" 
numa_= A[0]=="?"
numc=A[2:].count("C")
numc_= A[2:].count("?")

for i in range(1,n-1):
    #print(numa,numa_,numc,numc_)
    apro=cpro=0
    if A[i]=="B" or A[i]=="?":
        # for k in range(numa_+1):
        #     apro+= (((C(numa_,k)*pow(2,numa_-k,mod))%mod)*(numa+k))%mod
        # for k in range(numc_+1):
        #     cpro+= (((C(numc_,k)*pow(2,numc_-k,mod))%mod)*(numc+k))%mod
        #print(apro,cpro)
        apro= ((3*numa+numa_)*pow(3,(numa_-1),mod))%mod
        cpro= ((3*numc+numc_)*pow(3,(numc_-1),mod))%mod
        ans+= (apro*cpro)%mod
        ans%=mod
    if A[i] == "A":
        numa+=1
    if A[i]=="?":
        numa_+=1
    if A[i+1] =="C":
        numc-=1
    if A[i+1]=="?":
        numc_-=1
print(ans)