Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
from functools import lru_cache
INF = float("inf")

MOD = 998244353  # type: int


def main():
    A, B, C, D = map(int, input().split())

    @lru_cache(maxsize=None)
    def f(a, b):
        if a < A or b < B:
            return 0
        if a == A and b == B:
            return 1
        elif a == A:
            return pow(A, b-B, MOD)
        elif b == B:
            return pow(B, a-A, MOD)
        ans = (f(a-1, b)*b) % MOD
        ans += (f(a, b-1)*a) % MOD
        ans -= (f(a-1, b-1)*(a-1)*(b-1)) % MOD
        ans %= MOD
        return ans

    print(f(C, D))

    return


if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
from functools import lru_cache
INF = float("inf")

MOD = 998244353  # type: int


def main():
    A, B, C, D = map(int, input().split())
    DP = [[1]*(D-B+1) for _ in range(C-A+1)]

    for i in range(C-A+1):
        for j in range(D-B+1):
            if i == j == 0:
                continue
            DP[i][j] = 0
            if 0 <= i-1:
                DP[i][j] += (DP[i-1][j]*(j+B)) % MOD
                DP[i][j] %= MOD
            if 0 <= j-1:
                DP[i][j] += (DP[i][j-1]*(i+A)) % MOD
                DP[i][j] %= MOD
            if 0 <= i-1 and 0 <= j-1:
                DP[i][j] -= (DP[i-1][j-1]*(i+A-1)*(j+B-1)) % MOD
                DP[i][j] %= MOD
            # print(i, j, DP[i][j])
    print(DP[-1][-1] % MOD)
    # print(DP)

    # @lru_cache(maxsize=None)
    # def f(a, b):
    #     if a < A or b < B:
    #         return 0
    #     if a == A and b == B:
    #         return 1
    #     elif a == A:
    #         return pow(A, b-B, MOD)
    #     elif b == B:
    #         return pow(B, a-A, MOD)
    #     ans = (f(a-1, b)*b) % MOD
    #     ans += (f(a, b-1)*a) % MOD
    #     ans -= (f(a-1, b-1)*(a-1)*(b-1)) % MOD
    #     ans %= MOD
    #     return ans

    # print(f(C, D))

    return


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
from functools import lru_cache
INF = float("inf")

MOD = 998244353  # type: int


def main():
    A, B, C, D = map(int, input().split())
    DP = [[None]*(D-B) for _ in range(C-A)]

    def f(a, b):
        if a < A or b < B:
            return 0
        if a == A and b == B:
            return 1
        elif a == A:
            return pow(A, b-B, MOD)
        elif b == B:
            return pow(B, a-A, MOD)
        ans = (f(a-1, b)*b) % MOD
        ans += (f(a, b-1)*a) % MOD
        ans -= (f(a-1, b-1)*(a-1)*(b-1)) % MOD
        ans %= MOD
        return ans

    print(f(C, D))

    return


if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
from functools import lru_cache
INF = float("inf")

MOD = 998244353  # type: int


def main():
    A, B, C, D = map(int, input().split())
    DP = [[1]*(D-B+1) for _ in range(C-A+1)]

    for i in range(C-A+1):
        for j in range(D-B+1):
            if i == j == 0:
                continue
            DP[i][j] = 0
            if 0 <= i-1:
                DP[i][j] += (DP[i-1][j]*(j+B)) % MOD
                DP[i][j] %= MOD
            if 0 <= j-1:
                DP[i][j] += (DP[i][j-1]*(i+A)) % MOD
                DP[i][j] %= MOD
            if 0 <= i-1 and 0 <= j-1:
                DP[i][j] -= (DP[i-1][j-1]*(i+A-1)*(j+B-1)) % MOD
                DP[i][j] %= MOD
            # print(i, j, DP[i][j])
    print(DP[-1][-1] % MOD)
    # print(DP)

    # @lru_cache(maxsize=None)
    # def f(a, b):
    #     if a < A or b < B:
    #         return 0
    #     if a == A and b == B:
    #         return 1
    #     elif a == A:
    #         return pow(A, b-B, MOD)
    #     elif b == B:
    #         return pow(B, a-A, MOD)
    #     ans = (f(a-1, b)*b) % MOD
    #     ans += (f(a, b-1)*a) % MOD
    #     ans -= (f(a-1, b-1)*(a-1)*(b-1)) % MOD
    #     ans %= MOD
    #     return ans

    # print(f(C, D))

    return


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
from functools import lru_cache
INF = float("inf")

MOD = 998244353  # type: int


def main():
    A, B, C, D = map(int, input().split())

    @lru_cache(maxsize=None)
    def f(a, b):
        if a < A or b < B:
            return 0
        if a == A and b == B:
            return 1
        elif a == A:
            return A**(b-B) % MOD
        elif b == B:
            return B**(a-A) % MOD
        ans = f(a-1, b)*b
        ans %= MOD
        ans += f(a, b-1)*a
        ans %= MOD
        ans -= f(a-1, b-1)*(a-1)*(b-1)
        ans %= MOD
        return ans

    print(f(C, D))

    return


if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
from functools import lru_cache
INF = float("inf")

MOD = 998244353  # type: int


def main():
    A, B, C, D = map(int, input().split())
    DP = [[1]*(D-B+1) for _ in range(C-A+1)]

    for i in range(C-A+1):
        for j in range(D-B+1):
            if i == j == 0:
                continue
            DP[i][j] = 0
            if 0 <= i-1:
                DP[i][j] += (DP[i-1][j]*(j+B)) % MOD
                DP[i][j] %= MOD
            if 0 <= j-1:
                DP[i][j] += (DP[i][j-1]*(i+A)) % MOD
                DP[i][j] %= MOD
            if 0 <= i-1 and 0 <= j-1:
                DP[i][j] -= (DP[i-1][j-1]*(i+A-1)*(j+B-1)) % MOD
                DP[i][j] %= MOD
            # print(i, j, DP[i][j])
    print(DP[-1][-1] % MOD)
    # print(DP)

    # @lru_cache(maxsize=None)
    # def f(a, b):
    #     if a < A or b < B:
    #         return 0
    #     if a == A and b == B:
    #         return 1
    #     elif a == A:
    #         return pow(A, b-B, MOD)
    #     elif b == B:
    #         return pow(B, a-A, MOD)
    #     ans = (f(a-1, b)*b) % MOD
    #     ans += (f(a, b-1)*a) % MOD
    #     ans -= (f(a-1, b-1)*(a-1)*(b-1)) % MOD
    #     ans %= MOD
    #     return ans

    # print(f(C, D))

    return


if __name__ == '__main__':
    main()