Buggy python submission (verdict: Time Limit Exceeded):
#import time
#it = time.time()    
#print(d[C-A][D-B] % 998244353)
A, B, C, D = map(int,input().split())

d=[[0 for j in range(D-B+1)] for i in range(C-A+1)]
d[0][0]=1
for i in range(1,C-A+1):
  d[i][0] = B*d[i-1][0] % 998244353
for j in range(1,D-B+1):
  d[0][j] = A*d[0][j-1] % 998244353
#print(time.time()-it)  
for i in range(1,C-A+1):
  for j in range(1,D-B+1):
    #d[i][j]=( (((j+B)*d[i-1][j]) + (i+A)*d[i][j-1])  - ((i+A-1)*((j+B-1)*d[i-1][j-1]) % 998244353)% 998244353)% 998244353
    d[i][j]=((((j+B)*d[i-1][j]) + (i+A)*d[i][j-1])  - ((i+A-1)*((j+B-1)*d[i-1][j-1]) ))% 998244353
    #d[i][j]=d[i-1][j-1]*((i+A)*(j+B)-1)% 998244353
#print(time.time()-it)   
print(d[C-A][D-B] % 998244353)

Fixed submission:
import sys
import numpy as np
#from functools import lru_cache
 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
 
MOD = 998_244_353
 
def main(A, B, C, D):
	d = np.zeros((C + 1, D + 1), np.int64)
	d[A,B]=1
	for i in range(A+1,C+1):
  		d[i,B] = B*d[i-1,B] % MOD
	for j in range(B+1,D+1):
		d[A,j] = A*d[A,j-1] % MOD
 
	for i in range(A+1,C+1):
		for j in range(B+1,D+1):
			d[i,j]=((((j*d[i-1,j]) % MOD + i*d[i,j-1] % MOD) % MOD) -((i-1)*((j-1)*d[i-1,j-1] % MOD)% MOD)% MOD)
    
	return d[C,D] % MOD
          
"""    
    print(d[C][D] % MOD)
    dp = np.zeros((C + 1, D + 1), np.int64)
    dp[C, D] = 1
    for d in range(D, 0, -1):
        dp[C, d - 1] = dp[C, d] * C % MOD
    for c in range(C - 1, -1, -1):
        x = 0
        for d in range(D, -1, -1):
            dp[c, d] = (d * dp[c + 1, d] + x) % MOD
            x += dp[c + 1, d]
            x *= c
            x %= MOD
    return dp[A, B]
"""

if sys.argv[-1] == 'ONLINE_JUDGE':
    import numba
    from numba.pycc import CC
    i8 = numba.from_dtype(np.int64)
    signature = (i8, i8, i8, i8)
 
    cc = CC('my_module')
    cc.export('main', signature)(main)
    cc.compile()
 
from my_module import main
 
A, B, C, D = map(int, read().split())
print(main(A, B, C, D))

Buggy python submission (verdict: Time Limit Exceeded):
A, B, C, D = map(int,input().split())

d=[[0 for j in range(D+1)] for i in range(C+1)]
d[A][B]=1
for i in range(A+1,C+1):
  d[i][B] = B*d[i-1][B] % 998244353
for j in range(B+1,D+1):
  d[A][j] = A*d[A][j-1] % 998244353
 
for i in range(A+1,C+1):
  for j in range(B+1,D+1):
    d[i][j]=(((j*d[i-1][j]) % 998244353 + i*d[i][j-1] % 998244353) % 998244353 - ((i-1)*((j-1)*d[i-1][j-1]) % 998244353) % 998244353) % 998244353
    
print(d[C][D] % 998244353)

Fixed submission:
import sys
import numpy as np
#from functools import lru_cache
 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
 
MOD = 998_244_353
 
def main(A, B, C, D):
	d = np.zeros((C + 1, D + 1), np.int64)
	d[A,B]=1
	for i in range(A+1,C+1):
  		d[i,B] = B*d[i-1,B] % MOD
	for j in range(B+1,D+1):
		d[A,j] = A*d[A,j-1] % MOD
 
	for i in range(A+1,C+1):
		for j in range(B+1,D+1):
			d[i,j]=((((j*d[i-1,j]) % MOD + i*d[i,j-1] % MOD) % MOD) -((i-1)*((j-1)*d[i-1,j-1] % MOD)% MOD)% MOD)
    
	return d[C,D] % MOD
          
"""    
    print(d[C][D] % MOD)
    dp = np.zeros((C + 1, D + 1), np.int64)
    dp[C, D] = 1
    for d in range(D, 0, -1):
        dp[C, d - 1] = dp[C, d] * C % MOD
    for c in range(C - 1, -1, -1):
        x = 0
        for d in range(D, -1, -1):
            dp[c, d] = (d * dp[c + 1, d] + x) % MOD
            x += dp[c + 1, d]
            x *= c
            x %= MOD
    return dp[A, B]
"""

if sys.argv[-1] == 'ONLINE_JUDGE':
    import numba
    from numba.pycc import CC
    i8 = numba.from_dtype(np.int64)
    signature = (i8, i8, i8, i8)
 
    cc = CC('my_module')
    cc.export('main', signature)(main)
    cc.compile()
 
from my_module import main
 
A, B, C, D = map(int, read().split())
print(main(A, B, C, D))

Buggy python submission (verdict: Time Limit Exceeded):
A, B, C, D = map(int,input().split())

d=[[0 for j in range(D-B+1)] for i in range(C-A+1)]
d[0][0]=1
for i in range(1,C-A+1):
  d[i][0] = B*d[i-1][0] % 998244353
for j in range(1,D-B+1):
  d[0][j] = A*d[0][j-1] % 998244353
  
for i in range(1,C-A+1):
  for j in range(1,D-B+1):
    d[i][j]=((j+B)*d[i-1][j]) % 998244353 + (i+A)*d[i][j-1] % 998244353 - ((i+A-1)*((j+B-1)*d[i-1][j-1]) % 998244353)% 998244353
    
print(d[C-A][D-B] % 998244353)

Fixed submission:
import sys
import numpy as np
#from functools import lru_cache
 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
 
MOD = 998_244_353
 
def main(A, B, C, D):
	d = np.zeros((C + 1, D + 1), np.int64)
	d[A,B]=1
	for i in range(A+1,C+1):
  		d[i,B] = B*d[i-1,B] % MOD
	for j in range(B+1,D+1):
		d[A,j] = A*d[A,j-1] % MOD
 
	for i in range(A+1,C+1):
		for j in range(B+1,D+1):
			d[i,j]=((((j*d[i-1,j]) % MOD + i*d[i,j-1] % MOD) % MOD) -((i-1)*((j-1)*d[i-1,j-1] % MOD)% MOD)% MOD)
    
	return d[C,D] % MOD
          
"""    
    print(d[C][D] % MOD)
    dp = np.zeros((C + 1, D + 1), np.int64)
    dp[C, D] = 1
    for d in range(D, 0, -1):
        dp[C, d - 1] = dp[C, d] * C % MOD
    for c in range(C - 1, -1, -1):
        x = 0
        for d in range(D, -1, -1):
            dp[c, d] = (d * dp[c + 1, d] + x) % MOD
            x += dp[c + 1, d]
            x *= c
            x %= MOD
    return dp[A, B]
"""

if sys.argv[-1] == 'ONLINE_JUDGE':
    import numba
    from numba.pycc import CC
    i8 = numba.from_dtype(np.int64)
    signature = (i8, i8, i8, i8)
 
    cc = CC('my_module')
    cc.export('main', signature)(main)
    cc.compile()
 
from my_module import main
 
A, B, C, D = map(int, read().split())
print(main(A, B, C, D))

Buggy python submission (verdict: Time Limit Exceeded):
A, B, C, D = map(int,input().split())

d=[[0 for j in range(D+1)] for i in range(C+1)]
d[A][B]=1
for i in range(A+1,C+1):
  d[i][B] = B*d[i-1][B] % 998244353
for j in range(B+1,D+1):
  d[A][j] = A*d[A][j-1] % 998244353
 
for i in range(A+1,C+1):
  for j in range(B+1,D+1):
    d[i][j]=(j*d[i-1][j]) % 998244353 + i*d[i][j-1] % 998244353 - ((i-1)*((j-1)*d[i-1][j-1]) % 998244353)% 998244353
    
print(d[C][D] % 998244353)

Fixed submission:
import sys
import numpy as np
#from functools import lru_cache
 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
 
MOD = 998_244_353
 
def main(A, B, C, D):
	d = np.zeros((C + 1, D + 1), np.int64)
	d[A,B]=1
	for i in range(A+1,C+1):
  		d[i,B] = B*d[i-1,B] % MOD
	for j in range(B+1,D+1):
		d[A,j] = A*d[A,j-1] % MOD
 
	for i in range(A+1,C+1):
		for j in range(B+1,D+1):
			d[i,j]=((((j*d[i-1,j]) % MOD + i*d[i,j-1] % MOD) % MOD) -((i-1)*((j-1)*d[i-1,j-1] % MOD)% MOD)% MOD)
    
	return d[C,D] % MOD
          
"""    
    print(d[C][D] % MOD)
    dp = np.zeros((C + 1, D + 1), np.int64)
    dp[C, D] = 1
    for d in range(D, 0, -1):
        dp[C, d - 1] = dp[C, d] * C % MOD
    for c in range(C - 1, -1, -1):
        x = 0
        for d in range(D, -1, -1):
            dp[c, d] = (d * dp[c + 1, d] + x) % MOD
            x += dp[c + 1, d]
            x *= c
            x %= MOD
    return dp[A, B]
"""

if sys.argv[-1] == 'ONLINE_JUDGE':
    import numba
    from numba.pycc import CC
    i8 = numba.from_dtype(np.int64)
    signature = (i8, i8, i8, i8)
 
    cc = CC('my_module')
    cc.export('main', signature)(main)
    cc.compile()
 
from my_module import main
 
A, B, C, D = map(int, read().split())
print(main(A, B, C, D))

Buggy python submission (verdict: Time Limit Exceeded):
A, B, C, D = map(int,input().split())

d=[[0 for j in range(D+1)] for i in range(C+1)]
d[A][B]=1
for i in range(A+1,C+1):
  d[i][B] = B*d[i-1][B] % 998244353
for j in range(B+1,D+1):
  d[A][j] = A*d[A][j-1] % 998244353
 
for i in range(A+1,C+1):
  for j in range(B+1,D+1):
    d[i][j]=((j*d[i-1][j]) + i*d[i][j-1] -((i-1)*(j-1)*d[i-1][j-1])) % 998244353
    
print(d[C][D] % 998244353)

Fixed submission:
import sys
import numpy as np
#from functools import lru_cache
 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
 
MOD = 998_244_353
 
def main(A, B, C, D):
	d = np.zeros((C + 1, D + 1), np.int64)
	d[A,B]=1
	for i in range(A+1,C+1):
  		d[i,B] = B*d[i-1,B] % MOD
	for j in range(B+1,D+1):
		d[A,j] = A*d[A,j-1] % MOD
 
	for i in range(A+1,C+1):
		for j in range(B+1,D+1):
			d[i,j]=((((j*d[i-1,j]) % MOD + i*d[i,j-1] % MOD) % MOD) -((i-1)*((j-1)*d[i-1,j-1] % MOD)% MOD)% MOD)
    
	return d[C,D] % MOD
          
"""    
    print(d[C][D] % MOD)
    dp = np.zeros((C + 1, D + 1), np.int64)
    dp[C, D] = 1
    for d in range(D, 0, -1):
        dp[C, d - 1] = dp[C, d] * C % MOD
    for c in range(C - 1, -1, -1):
        x = 0
        for d in range(D, -1, -1):
            dp[c, d] = (d * dp[c + 1, d] + x) % MOD
            x += dp[c + 1, d]
            x *= c
            x %= MOD
    return dp[A, B]
"""

if sys.argv[-1] == 'ONLINE_JUDGE':
    import numba
    from numba.pycc import CC
    i8 = numba.from_dtype(np.int64)
    signature = (i8, i8, i8, i8)
 
    cc = CC('my_module')
    cc.export('main', signature)(main)
    cc.compile()
 
from my_module import main
 
A, B, C, D = map(int, read().split())
print(main(A, B, C, D))

Buggy python submission (verdict: Time Limit Exceeded):
A, B, C, D = map(int,input().split())

d=[[0 for j in range(D+1)] for i in range(C+1)]
d[A][B]=1
for i in range(A+1,C+1):
  d[i][B] = B*d[i-1][B] % 998244353
for j in range(B+1,D+1):
  d[A][j] = A*d[A][j-1] % 998244353
 
for i in range(A+1,C+1):
  for j in range(B+1,D+1):
    d[i][j]=(j*d[i-1][j]) % 998244353 + i*d[i][j-1] % 998244353 -((i-1)*(j-1)*d[i-1][j-1]) % 998244353
    
print(d[C][D] % 998244353)

Fixed submission:
import sys
import numpy as np
#from functools import lru_cache
 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
 
MOD = 998_244_353
 
def main(A, B, C, D):
	d = np.zeros((C + 1, D + 1), np.int64)
	d[A,B]=1
	for i in range(A+1,C+1):
  		d[i,B] = B*d[i-1,B] % MOD
	for j in range(B+1,D+1):
		d[A,j] = A*d[A,j-1] % MOD
 
	for i in range(A+1,C+1):
		for j in range(B+1,D+1):
			d[i,j]=((((j*d[i-1,j]) % MOD + i*d[i,j-1] % MOD) % MOD) -((i-1)*((j-1)*d[i-1,j-1] % MOD)% MOD)% MOD)
    
	return d[C,D] % MOD
          
"""    
    print(d[C][D] % MOD)
    dp = np.zeros((C + 1, D + 1), np.int64)
    dp[C, D] = 1
    for d in range(D, 0, -1):
        dp[C, d - 1] = dp[C, d] * C % MOD
    for c in range(C - 1, -1, -1):
        x = 0
        for d in range(D, -1, -1):
            dp[c, d] = (d * dp[c + 1, d] + x) % MOD
            x += dp[c + 1, d]
            x *= c
            x %= MOD
    return dp[A, B]
"""

if sys.argv[-1] == 'ONLINE_JUDGE':
    import numba
    from numba.pycc import CC
    i8 = numba.from_dtype(np.int64)
    signature = (i8, i8, i8, i8)
 
    cc = CC('my_module')
    cc.export('main', signature)(main)
    cc.compile()
 
from my_module import main
 
A, B, C, D = map(int, read().split())
print(main(A, B, C, D))

Buggy python submission (verdict: Time Limit Exceeded):
A, B, C, D = map(int,input().split())

d={}
d[(A,B)]=1
for i in range(A+1,C+1):
  d[(i,B)] = B*d[(i-1,B)] % 998244353
for j in range(B+1,D+1):
  d[(A,j)] = A*d[(A,j-1)] % 998244353
 
for i in range(A+1,C+1):
  for j in range(B+1,D+1):
    d[(i,j)]=(j*d[(i-1,j)]+i*d[(i,j-1)]-(i-1)*(j-1)*d[(i-1,j-1)]) % 998244353
    
print(d[(C,D)] % 998244353)

Fixed submission:
import sys
import numpy as np
#from functools import lru_cache
 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
 
MOD = 998_244_353
 
def main(A, B, C, D):
	d = np.zeros((C + 1, D + 1), np.int64)
	d[A,B]=1
	for i in range(A+1,C+1):
  		d[i,B] = B*d[i-1,B] % MOD
	for j in range(B+1,D+1):
		d[A,j] = A*d[A,j-1] % MOD
 
	for i in range(A+1,C+1):
		for j in range(B+1,D+1):
			d[i,j]=((((j*d[i-1,j]) % MOD + i*d[i,j-1] % MOD) % MOD) -((i-1)*((j-1)*d[i-1,j-1] % MOD)% MOD)% MOD)
    
	return d[C,D] % MOD
          
"""    
    print(d[C][D] % MOD)
    dp = np.zeros((C + 1, D + 1), np.int64)
    dp[C, D] = 1
    for d in range(D, 0, -1):
        dp[C, d - 1] = dp[C, d] * C % MOD
    for c in range(C - 1, -1, -1):
        x = 0
        for d in range(D, -1, -1):
            dp[c, d] = (d * dp[c + 1, d] + x) % MOD
            x += dp[c + 1, d]
            x *= c
            x %= MOD
    return dp[A, B]
"""

if sys.argv[-1] == 'ONLINE_JUDGE':
    import numba
    from numba.pycc import CC
    i8 = numba.from_dtype(np.int64)
    signature = (i8, i8, i8, i8)
 
    cc = CC('my_module')
    cc.export('main', signature)(main)
    cc.compile()
 
from my_module import main
 
A, B, C, D = map(int, read().split())
print(main(A, B, C, D))

Buggy python submission (verdict: Runtime Error):
A, B, C, D = map(int,input().split())

d={}
d[(A,B)]=1
for i in range(A+1,C+1):
  d[(i,B)] *= B*d[(i-1,B)] % 998244353
for j in range(B+1,D+1):
  d[(A,j)] *= A*d[(A,j-1)] % 998244353
 
for i in range(A+1,C+1):
  for j in range(B+1,D+1):
    d[(i,j)]=(j*d[(i-1,j)]+i*d[(i,j-1)]-(i-1)*(j-1)*d[(i-1,j-1)]) % 998244353
    
print(d[(C,D)] % 998244353)

Fixed submission:
import sys
import numpy as np
#from functools import lru_cache
 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
 
MOD = 998_244_353
 
def main(A, B, C, D):
	d = np.zeros((C + 1, D + 1), np.int64)
	d[A,B]=1
	for i in range(A+1,C+1):
  		d[i,B] = B*d[i-1,B] % MOD
	for j in range(B+1,D+1):
		d[A,j] = A*d[A,j-1] % MOD
 
	for i in range(A+1,C+1):
		for j in range(B+1,D+1):
			d[i,j]=((((j*d[i-1,j]) % MOD + i*d[i,j-1] % MOD) % MOD) -((i-1)*((j-1)*d[i-1,j-1] % MOD)% MOD)% MOD)
    
	return d[C,D] % MOD
          
"""    
    print(d[C][D] % MOD)
    dp = np.zeros((C + 1, D + 1), np.int64)
    dp[C, D] = 1
    for d in range(D, 0, -1):
        dp[C, d - 1] = dp[C, d] * C % MOD
    for c in range(C - 1, -1, -1):
        x = 0
        for d in range(D, -1, -1):
            dp[c, d] = (d * dp[c + 1, d] + x) % MOD
            x += dp[c + 1, d]
            x *= c
            x %= MOD
    return dp[A, B]
"""

if sys.argv[-1] == 'ONLINE_JUDGE':
    import numba
    from numba.pycc import CC
    i8 = numba.from_dtype(np.int64)
    signature = (i8, i8, i8, i8)
 
    cc = CC('my_module')
    cc.export('main', signature)(main)
    cc.compile()
 
from my_module import main
 
A, B, C, D = map(int, read().split())
print(main(A, B, C, D))

Buggy python submission (verdict: Time Limit Exceeded):
A, B, C, D = map(int,input().split())

d={}
for i in range(A,C+1):
  d[(i,B)] = B**(i-A) % 998244353
for j in range(B,D+1):
  d[(A,j)] = A**(j-B) % 998244353
 
for i in range(A+1,C+1):
  for j in range(B+1,D+1):
    d[(i,j)]=(j*d[(i-1,j)]+i*d[(i,j-1)]-(i-1)*(j-1)*d[(i-1,j-1)]) % 998244353
    
print(d[(C,D)] % 998244353)

Fixed submission:
import sys
import numpy as np
#from functools import lru_cache
 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
 
MOD = 998_244_353
 
def main(A, B, C, D):
	d = np.zeros((C + 1, D + 1), np.int64)
	d[A,B]=1
	for i in range(A+1,C+1):
  		d[i,B] = B*d[i-1,B] % MOD
	for j in range(B+1,D+1):
		d[A,j] = A*d[A,j-1] % MOD
 
	for i in range(A+1,C+1):
		for j in range(B+1,D+1):
			d[i,j]=((((j*d[i-1,j]) % MOD + i*d[i,j-1] % MOD) % MOD) -((i-1)*((j-1)*d[i-1,j-1] % MOD)% MOD)% MOD)
    
	return d[C,D] % MOD
          
"""    
    print(d[C][D] % MOD)
    dp = np.zeros((C + 1, D + 1), np.int64)
    dp[C, D] = 1
    for d in range(D, 0, -1):
        dp[C, d - 1] = dp[C, d] * C % MOD
    for c in range(C - 1, -1, -1):
        x = 0
        for d in range(D, -1, -1):
            dp[c, d] = (d * dp[c + 1, d] + x) % MOD
            x += dp[c + 1, d]
            x *= c
            x %= MOD
    return dp[A, B]
"""

if sys.argv[-1] == 'ONLINE_JUDGE':
    import numba
    from numba.pycc import CC
    i8 = numba.from_dtype(np.int64)
    signature = (i8, i8, i8, i8)
 
    cc = CC('my_module')
    cc.export('main', signature)(main)
    cc.compile()
 
from my_module import main
 
A, B, C, D = map(int, read().split())
print(main(A, B, C, D))

Buggy python submission (verdict: Time Limit Exceeded):
A, B, C, D = map(int,input().split())

d={}
for i in range(A,C+1):
  d[(i,B)] = B**(i-A)
for j in range(B,D+1):
  d[(A,j)] = A**(j-B)
 
for i in range(A+1,C+1):
  for j in range(B+1,D+1):
    d[(i,j)]=j*d[(i-1,j)]+i*d[(i,j-1)]-(i-1)*(j-1)*d[(i-1,j-1)]
    
print(d[(C,D)] % 998244353)

Fixed submission:
import sys
import numpy as np
#from functools import lru_cache
 
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
 
MOD = 998_244_353
 
def main(A, B, C, D):
	d = np.zeros((C + 1, D + 1), np.int64)
	d[A,B]=1
	for i in range(A+1,C+1):
  		d[i,B] = B*d[i-1,B] % MOD
	for j in range(B+1,D+1):
		d[A,j] = A*d[A,j-1] % MOD
 
	for i in range(A+1,C+1):
		for j in range(B+1,D+1):
			d[i,j]=((((j*d[i-1,j]) % MOD + i*d[i,j-1] % MOD) % MOD) -((i-1)*((j-1)*d[i-1,j-1] % MOD)% MOD)% MOD)
    
	return d[C,D] % MOD
          
"""    
    print(d[C][D] % MOD)
    dp = np.zeros((C + 1, D + 1), np.int64)
    dp[C, D] = 1
    for d in range(D, 0, -1):
        dp[C, d - 1] = dp[C, d] * C % MOD
    for c in range(C - 1, -1, -1):
        x = 0
        for d in range(D, -1, -1):
            dp[c, d] = (d * dp[c + 1, d] + x) % MOD
            x += dp[c + 1, d]
            x *= c
            x %= MOD
    return dp[A, B]
"""

if sys.argv[-1] == 'ONLINE_JUDGE':
    import numba
    from numba.pycc import CC
    i8 = numba.from_dtype(np.int64)
    signature = (i8, i8, i8, i8)
 
    cc = CC('my_module')
    cc.export('main', signature)(main)
    cc.compile()
 
from my_module import main
 
A, B, C, D = map(int, read().split())
print(main(A, B, C, D))