Buggy python submission (verdict: Runtime Error):
import math

n,m=map(int,input().split())
r=list(map(int,input().split()))
c=list(map(int,input().split()))
r.sort(reverse=True)
c.sort(reverse=True)
a=min(min(r),min(c))
dict1={}
dict2={}
for i in range(n):
    dict1.setdefault(r[i],0)
    dict1[r[i]]+=1
for i in range(m):
    dict2.setdefault(c[i],0)
    dict2[c[i]]+=1
x,y=0,0
ans=1
if dict1.get(n*m)*dict2.get(n*m)>1:
    print(0)
    exit()
for i in range(n*m,a-1,-1):
    table=x*y
    ex=table-(n*m-i)
    dy=dict1.get(i,0)
    dx=dict2.get(i,0)
    x+=dx
    y+=dy
    if dx*dy==1:
        ans*=1
    elif dx==0 and dy==1:
        ans*=x
    elif dy==0 and dx==1:
        ans*=y
    else:
        ans*=(x*y-(n*m-i))
b=math.factorial(a-1)
mod=10**9+7
ans*=(b%mod)
print(ans%mod)

Fixed submission:
n,m=map(int,input().split())
r=list(map(int,input().split()))
c=list(map(int,input().split()))
r.sort(reverse=True)
c.sort(reverse=True)
dict1={}
dict2={}
for i in range(n):
    dict1.setdefault(r[i],0)
    dict1[r[i]]+=1
for i in range(m):
    dict2.setdefault(c[i],0)
    dict2[c[i]]+=1
x,y=0,0
ans=1
mod=10**9+7
for i in range(n*m,0,-1):
    dy=dict1.get(i,0)
    dx=dict2.get(i,0)
    if dx*dy==1:
        x+=1
        y+=1
    elif dx==0 and dy==1:
        ans*=x
        y+=1
    elif dy==0 and dx==1:
        ans*=y
        x+=1
    else:
        ans*=(x*y-(n*m-i))
        ans%=mod
print(ans%mod)

Buggy python submission (verdict: Runtime Error):
n,m=map(int,input().split())
r=list(map(int,input().split()))
c=list(map(int,input().split()))
r.sort(reverse=True)
c.sort(reverse=True)
dict1={}
dict2={}
for i in range(n):
    dict1.setdefault(r[i],0)
    dict1[r[i]]+=1
for i in range(m):
    dict2.setdefault(c[i],0)
    dict2[c[i]]+=1
x,y=0,0
ans=1
if dict1.get(n*m)*dict2.get(n*m)>1:
    print(0)
    exit()
for i in range(n*m,0,-1):
    table=x*y
    ex=table-(n*m-i)
    dy=dict1.get(i,0)
    dx=dict2.get(i,0)
    x+=dx
    y+=dy
    if dx*dy==1:
        ans*=1
    elif dx==0 and dy==1:
        ans*=x
    elif dy==0 and dx==1:
        ans*=y
    else:
        ans*=(x*y-(n*m-i))
print(ans%(10**9+7))

Fixed submission:
n,m=map(int,input().split())
r=list(map(int,input().split()))
c=list(map(int,input().split()))
r.sort(reverse=True)
c.sort(reverse=True)
dict1={}
dict2={}
for i in range(n):
    dict1.setdefault(r[i],0)
    dict1[r[i]]+=1
for i in range(m):
    dict2.setdefault(c[i],0)
    dict2[c[i]]+=1
x,y=0,0
ans=1
mod=10**9+7
for i in range(n*m,0,-1):
    dy=dict1.get(i,0)
    dx=dict2.get(i,0)
    if dx*dy==1:
        x+=1
        y+=1
    elif dx==0 and dy==1:
        ans*=x
        y+=1
    elif dy==0 and dx==1:
        ans*=y
        x+=1
    else:
        ans*=(x*y-(n*m-i))
        ans%=mod
print(ans%mod)

Buggy python submission (verdict: Runtime Error):
n,m=map(int,input().split())
r=list(map(int,input().split()))
c=list(map(int,input().split()))
r.sort(reverse=True)
c.sort(reverse=True)
dict1={}
dict2={}
for i in range(n):
    dict1.setdefault(r[i],0)
    dict1[r[i]]+=1
for i in range(m):
    dict2.setdefault(c[i],0)
    dict2[c[i]]+=1
x,y=0,0
ans=1
if dict1.get(n*m)*dict2.get(n*m)>1:
    print(0)
    exit()
for i in range(n*m,0,-1):
    table=x*y
    ex=table-(n*m-i)
    dy=dict1.get(i,0)
    dx=dict2.get(i,0)
    print(ans,x,y)
    x+=dx
    y+=dy
    if dx*dy==1:
        ans*=1
    elif dx==0 and dy==1:
        ans*=x
    elif dy==0 and dx==1:
        ans*=y
    else:
        ans*=(x*y-(n*m-i))
print(ans%(10**9+7))

Fixed submission:
n,m=map(int,input().split())
r=list(map(int,input().split()))
c=list(map(int,input().split()))
r.sort(reverse=True)
c.sort(reverse=True)
dict1={}
dict2={}
for i in range(n):
    dict1.setdefault(r[i],0)
    dict1[r[i]]+=1
for i in range(m):
    dict2.setdefault(c[i],0)
    dict2[c[i]]+=1
x,y=0,0
ans=1
mod=10**9+7
for i in range(n*m,0,-1):
    dy=dict1.get(i,0)
    dx=dict2.get(i,0)
    if dx*dy==1:
        x+=1
        y+=1
    elif dx==0 and dy==1:
        ans*=x
        y+=1
    elif dy==0 and dx==1:
        ans*=y
        x+=1
    else:
        ans*=(x*y-(n*m-i))
        ans%=mod
print(ans%mod)