Buggy python submission (verdict: Time Limit Exceeded):
import sys

def MI(): return map(int, sys.stdin.readline().split())

md = 10 ** 9 + 7

n_max = 1005
fac = [1]
for i in range(1, n_max + 1): fac.append(fac[-1] * i % md)
ifac = [1] * (n_max + 1)
ifac[n_max] = pow(fac[n_max], md - 2, md)
for i in range(n_max - 1, 1, -1): ifac[i] = ifac[i + 1] * (i + 1) % md

def main():
    n, a, b, c, d = MI()
    dp = [0] * (n + 1)
    # dp[j]...i番目の人数の班まで決めて全体でj人が決まったときの場合の数
    dp[0] = 1
    for p in range(a, b + 1):
        for j in range(n, -1, -1):
            dp[j] += sum(dp[j - p * g] * fac[n - j + p * g] * ifac[n - j] * ifac[g] * pow(ifac[p], g, md) for g in
                         range(c, min(j // p, d) + 1))
            dp[j] %= md
    print(dp[n])

main()


Fixed submission:
import sys

def MI(): return map(int, sys.stdin.readline().split())

md = 10 ** 9 + 7

n_max = 1005
fac = [1]
for i in range(1, n_max + 1): fac.append(fac[-1] * i % md)
ifac = [1] * (n_max + 1)
ifac[n_max] = pow(fac[n_max], md - 2, md)
for i in range(n_max - 1, 1, -1): ifac[i] = ifac[i + 1] * (i + 1) % md

def main():
    n, a, b, c, d = MI()
    pn = b - a + 1  # 班人数の種類数
    dp = [[0] * (n + 1) for _ in range(pn + 1)]
    # dp[i][j]...i番目の人数の班まで決めて全体でj人が決まったときの場合の数
    dp[0][0] = 1
    ps = 0
    for i in range(pn):
        p = i + a  # 班人数
        low = n - (p + b) * (b - p + 1) * d // 2
        up = (a + p - 1) * (p - a) * d // 2
        for j in range(max(low, 0), min(n, up) + 1):
            pre = dp[i][j]
            if pre == 0: continue
            dp[i + 1][j] += pre
            dp[i + 1][j] %= md
            r = n - j  # 残りの人数
            for g in range(c, d + 1):
                if j + p * g > n: break
                dp[i + 1][j + p * g] += pre * fac[r] * ifac[r - p * g] * ifac[g] * pow(ifac[p], g, md)
                dp[i + 1][j + p * g] %= md
        ps += p
    print(dp[pn][n])

main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys

def MI(): return map(int, sys.stdin.readline().split())

md = 10 ** 9 + 7

n_max = 1005
fac = [1]
for i in range(1, n_max + 1): fac.append(fac[-1] * i % md)
ifac = [1] * (n_max + 1)
ifac[n_max] = pow(fac[n_max], md - 2, md)
for i in range(n_max - 1, 1, -1): ifac[i] = ifac[i + 1] * (i + 1) % md

def main():
    n, a, b, c, d = MI()
    pn = b - a + 1  # 班人数の種類数
    dp = [[0] * (n + 1) for _ in range(pn + 1)]
    # dp[i][j]...i番目の人数の班まで決めて全体でj人が決まったときの場合の数
    dp[0][0] = 1
    ps = 0
    for i in range(pn):
        p = i + a  # 班人数
        lim = n - (p + b) * (b - p + 1) * d // 2
        for j in range(max(lim, 0), min(n, ps * d) + 1):
            pre = dp[i][j]
            if pre == 0: continue
            dp[i + 1][j] += pre
            dp[i + 1][j] %= md
            r = n - j  # 残りの人数
            for g in range(c, d + 1):
                if j + p * g > n: break
                dp[i + 1][j + p * g] += pre * fac[r] * ifac[r - p * g] * ifac[g] * pow(ifac[p],g,md)
                dp[i + 1][j + p * g] %= md
        ps += p
    print(dp[pn][n])

main()


Fixed submission:
import sys

def MI(): return map(int, sys.stdin.readline().split())

md = 10 ** 9 + 7

n_max = 1005
fac = [1]
for i in range(1, n_max + 1): fac.append(fac[-1] * i % md)
ifac = [1] * (n_max + 1)
ifac[n_max] = pow(fac[n_max], md - 2, md)
for i in range(n_max - 1, 1, -1): ifac[i] = ifac[i + 1] * (i + 1) % md

def main():
    n, a, b, c, d = MI()
    pn = b - a + 1  # 班人数の種類数
    dp = [[0] * (n + 1) for _ in range(pn + 1)]
    # dp[i][j]...i番目の人数の班まで決めて全体でj人が決まったときの場合の数
    dp[0][0] = 1
    ps = 0
    for i in range(pn):
        p = i + a  # 班人数
        low = n - (p + b) * (b - p + 1) * d // 2
        up = (a + p - 1) * (p - a) * d // 2
        for j in range(max(low, 0), min(n, up) + 1):
            pre = dp[i][j]
            if pre == 0: continue
            dp[i + 1][j] += pre
            dp[i + 1][j] %= md
            r = n - j  # 残りの人数
            for g in range(c, d + 1):
                if j + p * g > n: break
                dp[i + 1][j + p * g] += pre * fac[r] * ifac[r - p * g] * ifac[g] * pow(ifac[p], g, md)
                dp[i + 1][j + p * g] %= md
        ps += p
    print(dp[pn][n])

main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

class mint:
    def __init__(self, x):
        self.__x = x % md

    def __str__(self):
        return str(self.__x)

    def __neg__(self):
        return mint(-self.__x)

    def __add__(self, other):
        if isinstance(other, mint): other = other.__x
        return mint(self.__x + other)

    def __sub__(self, other):
        if isinstance(other, mint): other = other.__x
        return mint(self.__x - other)

    def __rsub__(self, other):
        return mint(other - self.__x)

    def __mul__(self, other):
        if isinstance(other, mint): other = other.__x
        return mint(self.__x * other)

    __radd__ = __add__
    __rmul__ = __mul__

    def __truediv__(self, other):
        if isinstance(other, mint): other = other.__x
        return mint(self.__x * pow(other, md - 2, md))

    def __rtruediv__(self, other):
        return mint(other * pow(self.__x, md - 2, md))

    def __pow__(self, power, modulo=None):
        return mint(pow(self.__x, power, md))

md = 10**9+7

def nCr(com_n, com_r):
    if com_n < com_r: return 0
    return fac[com_n] * ifac[com_r] * ifac[com_n - com_r]

n_max = 1005
fac = [mint(1)]
for i in range(1, n_max + 1): fac.append(fac[-1] * i)
ifac = [mint(1)] * (n_max + 1)
ifac[n_max] /= fac[n_max]
for i in range(n_max - 1, 1, -1): ifac[i] = ifac[i + 1] * (i + 1)

def main():
    n,a,b,c,d=MI()
    pn=b-a+1    # 班人数の種類数
    dp=[[0]*(n+1) for _ in range(pn+1)]
    # dp[i][j]...i番目の人数の班まで決めて全体でj人が決まったときの場合の数
    dp[0][0]=mint(1)
    ps=0
    for i in range(pn):
        p=i+a   # 班人数
        lim=n-(p+b)*(b-p+1)*d//2
        for j in range(max(lim,0),min(n,ps*d)+1):
            pre=dp[i][j]
            if pre==0:continue
            dp[i+1][j]+=pre
            r=n-j   # 残りの人数
            for g in range(c,d+1):
                if j+p*g>n:break
                dp[i+1][j+p*g]+=pre*fac[r]*ifac[r-p*g]*ifac[g]*ifac[p]**g
        ps+=p
    print(dp[pn][n])

main()

Fixed submission:
import sys

def MI(): return map(int, sys.stdin.readline().split())

md = 10 ** 9 + 7

n_max = 1005
fac = [1]
for i in range(1, n_max + 1): fac.append(fac[-1] * i % md)
ifac = [1] * (n_max + 1)
ifac[n_max] = pow(fac[n_max], md - 2, md)
for i in range(n_max - 1, 1, -1): ifac[i] = ifac[i + 1] * (i + 1) % md

def main():
    n, a, b, c, d = MI()
    pn = b - a + 1  # 班人数の種類数
    dp = [[0] * (n + 1) for _ in range(pn + 1)]
    # dp[i][j]...i番目の人数の班まで決めて全体でj人が決まったときの場合の数
    dp[0][0] = 1
    ps = 0
    for i in range(pn):
        p = i + a  # 班人数
        low = n - (p + b) * (b - p + 1) * d // 2
        up = (a + p - 1) * (p - a) * d // 2
        for j in range(max(low, 0), min(n, up) + 1):
            pre = dp[i][j]
            if pre == 0: continue
            dp[i + 1][j] += pre
            dp[i + 1][j] %= md
            r = n - j  # 残りの人数
            for g in range(c, d + 1):
                if j + p * g > n: break
                dp[i + 1][j + p * g] += pre * fac[r] * ifac[r - p * g] * ifac[g] * pow(ifac[p], g, md)
                dp[i + 1][j + p * g] %= md
        ps += p
    print(dp[pn][n])

main()