Problem:
 Score : 600 points    Problem Statement You are given an integer sequence of length n+1 , a_1,a_2,...,a_{n+1} , which consists of the n integers 1,...,n .
It is known that each of the n integers 1,...,n appears at least once in this sequence.  For each integer k=1,...,n+1 , find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k , modulo 10^9+7 .      Notes   If the contents of two subsequences are the same, they are not separately counted even if they originate from different positions in the original sequence.    A subsequence of a sequence a with length k is a sequence obtained by selecting k of the elements of a and arranging them without changing their relative order. For example, the sequences 1,3,5 and 1,2,3 are subsequences of 1,2,3,4,5 , while 3,1,2 and 1,10,100 are not.        Constraints  1 \leq n \leq 10^5  1 \leq a_i \leq n  Each of the integers 1,...,n appears in the sequence.  n and a_i are integers.         Input Input is given from Standard Input in the following format:  n  a_1  a_2 ... a_{n+1}       Output Print n+1 lines.
The k -th line should contain the number of the different subsequences of the given sequence with length k , modulo 10^9+7 .        Sample Input 1 3
1 2 1 3      Sample Output 1 3
5
4
1  There are three subsequences with length 1 : 1 and 2 and 3 .  There are five subsequences with length 2 : 1,1 and 1,2 and 1,3 and 2,1 and 2,3 .  There are four subsequences with length 3 : 1,1,3 and 1,2,1 and 1,2,3 and 2,1,3 .  There is one subsequence with length 4 : 1,2,1,3 .       Sample Input 2 1
1 1      Sample Output 2 1
1  There is one subsequence with length 1 : 1 .  There is one subsequence with length 2 : 1,1 .       Sample Input 3 32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9      Sample Output 3 32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1  Be sure to print the numbers modulo 10^9+7 .

Solution (Python):
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
from operator import mul
from functools import reduce


sys.setrecursionlimit(2147483647)
INF = 10 ** 20
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def I(): return int(sys.stdin.buffer.readline())
def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()
def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 1000000007


n = I() + 1
A = LI()


fac = [1] * (n + 1)
inv = [1] * (n + 1)
for j in range(1, n + 1):
    fac[j] = fac[j-1] * j % mod


inv[n] = pow(fac[n], mod-2, mod)
for j in range(n-1, -1, -1):
    inv[j] = inv[j+1] * (j+1) % mod


def comb(n, r):
    if r > n or n < 0 or r < 0:
        return 0
    return fac[n] * inv[n - r] * inv[r] % mod


D = defaultdict(lambda:-1)
for i in range(n + 1):
    if D[A[i]] != -1:
        l = D[A[i]]
        r = n - i - 1
        break
    else:
        D[A[i]] = i


for k in range(1, n + 1):
    print((comb(n, k) - comb(l + r, k - 1)) % mod)

Solution (Python):
class combination():
    
    def __init__(self, n, mod):
        self.n = n
        self.fac = [1] * (n + 1)
        self.inv = [1] * (n + 1)
        for j in range(1, n + 1):
            self.fac[j] = self.fac[j - 1] * j % mod

        self.inv[n] = pow(self.fac[n], mod - 2, mod)
        for j in range(n - 1, -1, -1):
            self.inv[j] = self.inv[j + 1] * (j + 1) % mod

    def comb(self, n, r, mod):
        if r > n or n < 0 or r < 0:
            return 0
        return self.fac[n] * self.inv[n - r] * self.inv[r] % mod

def examD(mod):
    N = I()
    a = LI()
    c = Counter(a)
    db = c.most_common()[0][0]
    curL = a.index(db)
    curR = a.index(db, curL + 1)
    L = curL; M = curR-curL-1;  R = N - curR


    C = combination(N+1,mod)
    ans = []
    ans.append(N)
    for i in range(2,N+2):
        cur = C.comb(N+1,i,mod)
        if N-1-M-(i-1)>=0:
            cur -= C.comb(N-1-M,i-1,mod)
        if cur<0:
            cur += mod
        ans.append(cur)
    for v in ans:
        print(v)

import sys
import copy
import bisect
import heapq
from collections import Counter,defaultdict,deque
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def S(): return sys.stdin.readline().strip()
mod = 10**9 + 7
inf = float('inf')

examD(mod)

Solution (Python):

import sys
input = sys.stdin.buffer.readline


from collections import defaultdict

con = 10 ** 9 + 7

def getlist():
	return list(map(int, input().split()))

class Combination(object):
	def __init__(self, N, con):
		self.fac = [0] * (N + 1)
		self.inv = [0] * (N + 1)
		self.finv = [0] * (N + 1)
		self.fac[0], self.fac[1] = 1, 1
		self.inv[1] = 1
		self.finv[0], self.finv[1] = 1, 1

		
		for i in range(2, N + 1):
			self.fac[i] = self.fac[i - 1] * i % con
			self.inv[i] = self.inv[con % i] * (con - (con // i)) % con
			self.finv[i] = self.finv[i - 1] * self.inv[i] % con

	def com(self, N, k):
		return (self.fac[N] * self.finv[k] * self.finv[N - k]) % con


def main():
	N = int(input())
	A = getlist()
	x = 0
	y = 0
	D = defaultdict(lambda: -1)
	for i in range(N + 1):
		if D[A[i]] == -1:
			D[A[i]] = i
		else:
			x = D[A[i]]
			y = i
			break
	n = y - x
	if N - n == 0:
		C1 = Combination(N + 1, con)
		print(C1.com(N + 1, i) - 1)
		for i in range(2, N + 2):
			print(C1.com(N + 1, i))
	else:
		C1 = Combination(N + 1, con)
		C2 = Combination(N - n, con)
		for i in range(1, N - n + 2):
			print((C1.com(N + 1, i) - C2.com(N - n, i - 1)) % con)
		for i in range(N - n + 2, N + 2):
			print(C1.com(N + 1, i))

if __name__ == '__main__':
	main()

Solution (Python):
import time
st_time=time.time()

from heapq import heappush, heappop
from collections import deque,defaultdict,Counter
import itertools
from itertools import permutations,combinations
import sys
import bisect
import string
import math
import random
def I():
    return int(input())
def MI():
    return map(int,input().split())
def LI():
    return [int(i) for i in input().split()]
def LI_():
    return [int(i)-1 for i in input().split()]
def show(*inp,end='\n'):
    if show_flg:
        print(*inp,end=end)
YN=['Yes','No']
mo=10**9+7
inf=float('inf')
ts=time.time()
sys.setrecursionlimit(10**6)

show_flg=False
show_flg=True

class Comb:
    def __init__(self,n,mo=10**9+7):
        self.fac=[0]*(n+1)
        self.inv=[1]*(n+1)
        self.fac[0]=1
        self.fact(n)
        for i in range(2,n+1):
            self.inv[n]*=i
            self.inv[n]%=mo
        self.inv[n]=pow(self.inv[n],mo-2,mo)
        for i in range(1,n):
            self.inv[n-i]=self.inv[n-i+1]*(n-i+1)%mo
        return
    
    def fact(self,n):
        if self.fac[n]!=0:
            return self.fac[n]
        self.fac[n]=n*self.fact(n-1)%mo
        return self.fac[n]

    def invf(self,n):
        return self.inv[n]

    def comb(self,x,y):
        if y<0 or y>x:
            return 0
        return self.fac[x]*self.inv[x-y]*self.inv[y]%mo
    
n=int(input())
a=[int(i) for i in input().split()]

cm=Comb(n+1)
c=Counter(a)
db=c.most_common()[0][0]
fst=a.index(db)
lst=a.index(db,fst+1)
x=n+1-(lst-fst+1)

for i in range(1,n+2):
    ans=cm.comb(n+1,i)-cm.comb(x,i-1)
    print(ans%mo)

Solution (Python):
mod=10**9+7
MAX=10**5+1000

g1=[1,1]
g2=[1,1]
for i in range(2,MAX+1):
    num_1=g1[-1]*i%mod
    g1.append(num_1)
    g2.append(pow(num_1,mod-2,mod))
    
def cmb(n,r,MOD):
    return g1[n]*g2[r]*g2[n-r]%MOD

n=int(input())
a=list(map(int,input().split()))
data=[0]*(n+1)
for i in range(n+1):
    data[a[i]]+=1
for i in range(1,n+1):
    if data[i]==2:
        b=i
        break
l=[]
for i in range(n+1):
    if a[i]==b:
        l.append(i)
c=l[1]-l[0]+1
for k in range(1,n+3-c):
    ans=cmb(n+1,k,mod)-cmb(n+1-c,k-1,mod)
    print(ans%mod)
for k in range(n+3-c,n+2):
    ans=cmb(n+1,k,mod)
    print(ans)

Solution (Python):
def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 
N = 10**5+1
g1 = [1, 1] 
g2 = [1, 1] 
inverse = [0, 1] 

for i in range( 2, N + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )
    
n=int(input())
a=list(map(int,input().split()))
data=[0]*(n+1)
for i in range(n+1):
    data[a[i]]+=1
for i in range(1,n+1):
    if data[i]==2:
        b=i
        break
l=[]
for i in range(n+1):
    if a[i]==b:
        l.append(i)
c=l[1]-l[0]+1
for k in range(1,n+3-c):
    ans=cmb(n+1,k,mod)-cmb(n+1-c,k-1,mod)
    print(ans%mod)
for k in range(n+3-c,n+2):
    ans=cmb(n+1,k,mod)
    print(ans)

Solution (Python):
class Factorial:
    def __init__(self, n, mod):
        self.f = [1]
        self.mod = mod
        for j in range(1, n + 1):
            self.f.append(self.f[-1] * j % mod)
        self.i = [pow(self.f[-1], mod - 2, mod)]
        for j in range(n, 0, -1):
            self.i.append(self.i[-1] * j % mod)
        self.i.reverse()
    def factorial(self, j):
        return self.f[j]
    def ifactorial(self, j):
        return self.i[j]
    def comb(self, n, k):
        return self.f[n] * self.i[n - k] % self.mod * self.i[k] % self.mod if n >= k else 0

from collections import *
MOD = 10 ** 9 + 7


n, *a = map(int, open(0).read().split())
v, _ = Counter(a).most_common(1)[0]
l = -1
for i, b in enumerate(a):
    if b == v:
        if l < 0:l = i
        else: r = n - i
c = Factorial(n + 1, MOD).comb
for k in range(n + 1):
    print ((c(n + 1, k + 1) - c(l + r, k)) % MOD)

Solution (Python):
N=int(input())
A=list(map(int,input().split()))
p=[-1]*N
x=0
for i in range(N):
    if p[A[i]-1]==-1:
        p[A[i]-1]=i
    else:
        x=p[A[i]-1]+N-i
        break
m=10**9+7
print(N)
a,b=N+1,1
def sub(a,b):
    return (a-b)%m
def mul(a,b):
    return ((a%m)*(b%m))%m
def div(a,b):
    return mul(a,pow(b,m-2,m))
for k in range(2,N+2):
    a=div(a*(N+2-k),k)
    b=div(b*(x+2-k),k-1)
    print(sub(a,b))

Solution (Python):
MOD = 10 ** 9 + 7
n = int(input())
a = list(map(int, input().split()))
lst = [-1] * n


for i in range(n + 1):
    if lst[a[i] - 1] != -1:
        first = lst[a[i] - 1]
        second = i
        break
    lst[a[i] - 1] = i


left = first
right = n - second

U = 10 ** 5 + 1
def power_mod(a, n):
    if n == 0:
        return 1
    x = power_mod(a//2)

def make_fact(fact, fact_inv):
    for i in range(1, U + 1):
        fact[i] = (fact[i - 1] * i) % MOD
    fact_inv[U] = pow(fact[U], MOD - 2, MOD)
    for i in range(U, 0, -1):
        fact_inv[i - 1] = (fact_inv[i] * i) % MOD

def comb(n, k):
    if k < 0 or n < k:
        return 0
    x = fact[n]
    x *= fact_inv[k]
    x %= MOD
    x *= fact_inv[n - k]
    x %= MOD
    return x

fact = [1] * (U + 1)
fact_inv = [1] * (U + 1)
make_fact(fact, fact_inv)

for i in range(1, n + 2):
    ans = comb(n + 1, i) - comb(left + right, i - 1)
    print (ans % MOD)

Solution (Python):
import collections
mod = 10**9+7
fac = [1]
caf = [1]
n=int(input())

def pow(n,p):
    res=1
    while p >0:
        if p%2==0:
            n = n**2 % mod
            p //= 2
        else:
            res = res * n % mod
            p -= 1
    return res % mod

for i in range(1,n+2):
    fac.append((fac[i-1]*i)%mod)
    caf.append(pow(fac[i],mod-2)%mod)

def ncr(n,r):
    if n < r: return 0
    return fac[n]*caf[r]*caf[n-r]

def main():
    global n
    a=list(map(int,input().split()))

    ca= collections.Counter(a)
    tyo= ca.most_common()[0][0]
    kaburi=[i for i, x in enumerate(a) if x == tyo]

    for i in range(1,n+2):
        print((ncr(n+1,i)-ncr(n+1-(kaburi[1]-kaburi[0]+1),i-1))%mod)

main()

Solution (Python):
import collections
mod = 10**9+7
fac = [1]
caf = [1]
n=int(input())

def pow(n,p):
    res=1
    while p >0:
        if p%2==0:
            n = n**2 % mod
            p //= 2
        else:
            res = res * n % mod
            p -= 1
    return res % mod

for i in range(1,n+2):
    fac.append((fac[i-1]*i)%mod)
    caf.append(pow(fac[i],mod-2)%mod)

def ncr(n,r):
    if n < r: return 0
    return fac[n]*caf[r]*caf[n-r]

def main():
    global n
    a=list(map(int,input().split()))

    ca= collections.Counter(a)
    tyo= ca.most_common()[0][0]
    kaburi=[i for i, x in enumerate(a) if x == tyo]

    for i in range(1,n+2):
        print((ncr(n+1,i)-ncr(n+1-(kaburi[1]-kaburi[0]+1),i-1))%mod)

main()

Solution (Python):
import sys
from collections import defaultdict
from math import factorial
input = sys.stdin.buffer.readline
mod = 10**9+7


nmax = 10 ** 5 + 2  
fac = [0] * (nmax + 1)
finv = [0] * (nmax + 1)
inv = [0] * (nmax + 1)
fac[0] = 1
fac[1] = 1
finv[0] = 1
finv[1] = 1
inv[1] = 1
for i in range(2, nmax):
    fac[i] = fac[i - 1] * i % mod
    inv[i] = mod - inv[mod % i] * (mod // i) % mod
    finv[i] = finv[i - 1] * inv[i] % mod


def comb(n, r):
    if n < r:
        return 0
    else:
        return (fac[n] * ((finv[r] * finv[n - r]) % mod)) % mod


N = int(input())
a = list(map(int, input().split()))

pos = defaultdict(lambda: -1)
for i in range(N+1):
    if pos[a[i]] == -1:
        pos[a[i]] = i
    else:
        same = (pos[a[i]], i)
        break

for k in range(1, N+2):
    print((comb(N+1, k) - comb(same[0] + (N-same[1]), k-1))%mod)

Solution (Python):
MOD=10**9+7
p=100009
fact=[0]*p 
fact[0]=1 
for i in range(1,p):
    fact[i]=(fact[i-1]*i)%MOD
def MI(a,MOD):
    return pow(a,MOD-2,MOD)
def nck(n, k,MOD):
    if k<0:
        return 0 
    if n==k or k==0:
        return 1 
    if n<k:
        return 0 
    return (fact[n]*MI(fact[k],MOD)%MOD*MI(fact[n-k],MOD)%MOD)%MOD

n=int(input())
l=[int(i) for i in input().split()]
from collections import Counter
c=Counter(l)
for i  in c:
    if c[i]>=2:
        ans=i 
        break 
ind1=-1 
ind2=-1 
for i in range(n+1):
    if l[i]==ans:
        if ind1==-1:
            ind1= i 
        else: 
            ind2=i 
MOD=10**9+7 
for i in range(1,n+2):
    a=nck(n+1,i,MOD)
    b=nck(n-(ind2-ind1),i-1,MOD)
    print((a-b+MOD)%MOD)

Solution (Python):
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
from operator import mul
from functools import reduce


INF = float('inf')
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return sys.stdin.readline().strip()
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 1000000007


n = I() + 1
A = LI()
D = defaultdict(lambda:-1)
for i in range(n):
    if D[A[i]] != -1:
        l = D[A[i]]
        r = n - i - 1
        break
    else:
        D[A[i]] = i


fac = [1] * (n + 1)
inv = [1] * (n + 1)
for j in range(1, n + 1):
    fac[j] = fac[j-1] * j % mod


inv[n] = pow(fac[n], mod-2, mod)
for j in range(n-1, -1, -1):
    inv[j] = inv[j+1] * (j+1) % mod


def comb(n, r):
    if r > n or n < 0 or r < 0:
        return 0
    return fac[n] * inv[n - r] * inv[r] % mod


for j in range(1, n + 1):
    print((comb(n, j) - comb(r + l, j - 1)) % mod)

Solution (Python):
def find_power(n):
    
    powlist=[0]*(n+1)
    powlist[0]=1
    powlist[1]=1
    for i in range(2,n+1):
        powlist[i]=powlist[i-1]*i%(10**9+7)
    return powlist

def find_inv_power(n):
    
    powlist=find_power(n)
    check=powlist[-1]
    first=1
    uselist=[0]*(n+1)
    secondlist=[0]*30
    secondlist[0]=check
    secondlist[1]=check**2
    for i in range(28):
        secondlist[i+2]=(secondlist[i+1]**2)%(10**9+7)
    a=format(10**9+5,"b")
    for j in range(30):
        if a[29-j]=="1":
            first=(first*secondlist[j])%(10**9+7)
    uselist[n]=first
    for i in range(n,0,-1):
        uselist[i-1]=(uselist[i]*i)%(10**9+7)
    return uselist

n=int(input())
lists=list(map(int,input().split()))
import collections
c=collections.Counter(lists)
d=c.most_common()
number=d[0][0]
listss=[]
for i in range(n+1):
    if lists[i]==number:
        listss.append(i+1)
a,b=listss[0],listss[1]

powlist=find_power(n+1)
invlist=find_inv_power(n+1)
def combi(n,r):
    a=powlist
    b=invlist
    if n<r:
        return 0
    elif n>=r:
        return (a[n]*b[r]*b[n-r])%(10**9+7)
    
for i in range(1,n+2):
    if i==1:
        print(n)
    elif 2<=i and i<=n+1-(b-a):
        print((combi(n-1,i)+combi(n-1,i-2)+2*combi(n-1,i-1)-combi(n+a-b,i-1))%(10**9+7))
    else:
        print(combi(n+1,i)%(10**9+7))

Solution (Python):
from collections import Counter, defaultdict
import sys
sys.setrecursionlimit(10 ** 5 + 10)

from math import factorial
import heapq, bisect
import math
import itertools

import queue
from collections import deque

def comb(n, r, mod, bunsi):
    if r > n:
        return 0
    ans = bunsi[n] * pow(bunsi[r], mod - 2, mod) * pow(bunsi[n - r], mod - 2, mod)
    return ans


def main():
    num = int(input())
    data = list(map(int, input().split()))

    mod = 10 ** 9 + 7

    count_data = Counter(data)
    count_data = sorted(count_data.items(), key=lambda x: -x[1])
    two_num = count_data[0][0]

    flg = 0
    left, mid, right = 0, 0, 0

    for i in range(num + 1):
        if data[i] == two_num:
            flg += 1
        elif flg == 0:
            left += 1
        elif flg == 1:
            mid += 1
        else:
            right += 1

    bunsi = [0 for i in range(num + 10)]
    bunsi[1] = 1
    bunsi[0] = 1
    for i in range(2, num + 10):
        bunsi[i] = (bunsi[i - 1] * i) % mod


    for now_num in range(1, num + 2):
        ans = 0
        if now_num == 1:
            ans += num
        elif now_num == 2:
            ans += comb(num - 1, 2, mod, bunsi)
            ans += 1
            ans += left + right + mid * 2
        else:
            ans += comb(num - 1, now_num, mod, bunsi)
            ans += comb(num - 1, now_num - 2, mod, bunsi)
            ans += comb(num - 1, now_num - 1, mod, bunsi) * 2 - comb(left, now_num - 1, mod, bunsi) - comb(right, now_num - 1, mod, bunsi)
            kari = comb(left + right, now_num - 1, mod, bunsi) - comb(left, now_num - 1, mod, bunsi) - comb(right, now_num - 1, mod, bunsi)
            ans -= kari

        ans %= mod
        print(ans)


if __name__ == '__main__':
    main()

Solution (Python):
def d_11(MOD=10**9 + 7):
    class Combination(object):
        """参考: https://harigami.net/contents?id=5f169f85-5707-4137-87a5-f0068749d9bb"""
        __slots__ = ["mod", "factorial", "inverse"]

        def __init__(self, max_n: int = 10**6, mod: int = 10**9 + 7):
            fac, inv = [1], []
            fac_append, inv_append = fac.append, inv.append

            for i in range(1, max_n + 1):
                fac_append(fac[-1] * i % mod)

            inv_append(pow(fac[-1], mod - 2, mod))

            for i in range(max_n, 0, -1):
                inv_append(inv[-1] * i % mod)

            self.mod, self.factorial, self.inverse = mod, fac, inv[::-1]

        def combination(self, n, r):
            if n < 0 or r < 0 or n < r:
                return 0
            return self.factorial[n] * self.inverse[r] * self.inverse[n - r] % self.mod

    N = int(input())
    A = [int(i) for i in input().split()]
    
    appeared = set()
    for k, a in enumerate(A):
        if a in appeared:
            left, right = A.index(a), k
            break
        appeared.add(a)

    c = Combination(N + 1).combination
    ans = [(c(N + 1, k) - c(N - (right - left), k - 1)) % MOD for k in range(1, N + 2)]
    return '\n'.join(map(str, ans))

print(d_11())

Solution (Python):
def d_11(MOD=10**9 + 7):
    from collections import Counter

    class Combination(object):
        """参考: https://harigami.net/contents?id=5f169f85-5707-4137-87a5-f0068749d9bb"""
        __slots__ = ["mod", "factorial", "inverse"]

        def __init__(self, max_n: int = 10**6, mod: int = 10**9 + 7):
            fac, inv = [1], []
            fac_append, inv_append = fac.append, inv.append

            for i in range(1, max_n + 1):
                fac_append(fac[-1] * i % mod)

            inv_append(pow(fac[-1], mod - 2, mod))

            for i in range(max_n, 0, -1):
                inv_append(inv[-1] * i % mod)

            self.mod, self.factorial, self.inverse = mod, fac, inv[::-1]

        def combination(self, n, r):
            if n < 0 or r < 0 or n < r:
                return 0
            return self.factorial[n] * self.inverse[r] * self.inverse[n - r] % self.mod

    N = int(input())
    A = [int(i) for i in input().split()]
    
    c = Counter(A).most_common(n=1)[0][0]  
    index = [i for i, x in enumerate(A) if x == c]  
    left = index[0] + 1
    right = index[1] + 1

    comb = Combination(N + 1).combination
    ans = [(comb(N + 1, k) - comb(N - (right - left), k - 1)) % MOD for k in range(1, N + 2)]
    return '\n'.join(map(str, ans))

print(d_11())

Solution (Python):
from math import factorial as f
from collections import Counter as co
n=int(input())
a=list(map(int,input().split()))
mod=10**9+7
d=co(a)
keys=[k for k,v in d.items() if v==2]
dbl=keys[0]
ll=[i for i,x in enumerate(a) if x==dbl]
b=ll[1]-ll[0]
m=n-b

def pf(x,y,p):
  if y==0: return 1
  if y%2==0:
    d=pf(x,y//2,p)
    return d*d%p
  if y%2==1:
    return (x*pf(x,y-1,p))%p

facl=[1]
for i in range(1,n+2):
  facl.append(facl[i-1]*i%mod)
invl=[1]*(n+2)
for i in range(1,n+2):
  invl[i]=pf(facl[i],mod-2,mod)

def comb(x,k,p):
  if x<0 or k<0 or x<k: return 0
  if x==0 or k==0: return 1
  return (facl[x]*invl[k]*invl[x-k])%mod

for k in range(1,n+2):
  print((comb(n+1,k,mod)-comb(m,k-1,mod))%mod)

Solution (Python):
from collections import Counter

mod = 10**9 + 7

def init(n):
    
    global factorial, inverse
    
    factorial = [1]*(n+1)
    inverse = [1]*(n+1)

    fact = 1
    for p in range(1,n+1):
        fact *= p
        fact %= mod
        factorial[p] = fact

    inv = pow(fact, mod-2, mod)
    inverse[n] = inv
    for p in range(2,n+1)[::-1]:
        inv *= p
        inv %= mod
        inverse[p-1] = inv

def comb(n,r):
    if n < r:
        return 0
    return factorial[n] * inverse[n-r] * inverse[r] % mod

n = int(input())
a = list(map(int,input().split()))

b = Counter(a).most_common()[0][0]
pos = []
for i, ai in enumerate(a):
    if ai == b:
        pos.append(i)

l, r = pos
L, R = l, n-r

init(n+1)

for k in range(1, n+2):
    ans = (comb(n+1, k) - comb(L+R, k-1)) % mod
    print(ans)

Solution (Python):
n = int(input())
a = list(map(int,input().split()))
search = [-1 for i in range(n)]
l,r = -1,-1
for i,x in enumerate(a):
    if search[x-1] == -1:
        search[x-1] = i
    else:
        l = search[x-1]
        r = i

p = 10**9 + 7


comb1 = [0 for _ in range(n+1)]
comb1[0] = n+1
x = n+1
for i in range(1,n+1):
    x = (x*(n-i+1))%p
    x = (x*pow(i+1,p-2,p))%p
    comb1[i] = x

comb2 = [0 for _ in range(n+1)]
comb2[0] = 1
x = 1
for i in range(1,l+n-r+1):
    x = (x*(n+l-r-i+1))%p
    x = (x*pow(i,p-2,p))%p
    comb2[i] = x

for i in range(n+1):
    ans = comb1[i]-comb2[i]

    print(ans%p)

Solution (Python):



import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(1000000)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))


def comb(n,r):
    if n - r < 0:
        return 0
    return fact[n] * invfact[r] * invfact[n-r] % mod

n = I()
a = LI()
cnt = [0]*(n+1)
for i in range(n+1):
    if cnt[a[i]]:
        a = cnt[a[i]]
        b = i+1
        break
    else:
        cnt[a[i]] = i+1

fact = [1]*(n+2)
invfact = [1]*(n+2)
for i in range(1,n+2):
    fact[i] = i*fact[i-1] % mod
    invfact[i] = invfact[i-1] * pow(i,mod-2,mod) % mod

for i in range(n+1):
    res = 0
    res = (res + comb(n+1,i+1)) % mod
    res = (res - comb((a-1)+(n+1-b),i)) % mod
    print(res)

Solution (Python):



import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(1000000)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
def f(a, b):
    if b == 0: 
        return 1
    if b % 2 == 0:
        d = f(a, b // 2)
        return d * d % mod
    if b % 2 == 1:
        return (a * f(a, b - 1)) % mod


def comb(n,r):
    if n - r < 0:
        return 0
    return fact[n] * invfact[r] * invfact[n-r] % mod

n = I()
a = LI()
cnt = [0]*(n+1)
for i in range(n+1):
    if cnt[a[i]]:
        a = cnt[a[i]]
        b = i+1
        break
    else:
        cnt[a[i]] = i+1

fact = [1]*(n+2)
invfact = [1]*(n+2)
for i in range(1,n+2):
    fact[i] = i*fact[i-1] % mod
    invfact[i] = invfact[i-1] * f(i,mod-2) % mod

for i in range(n+1):
    res = 0
    res = (res + comb(n+1,i+1)) % mod
    res = (res - comb((a-1)+(n+1-b),i)) % mod
    print(res)

Solution (Python):
n = int(input())
a = list(map(int, input().split()))
mod = 10**9+7
res = [-1] * (n+1)
for i in range(n+1):
    if res[a[i]] == -1:
        res[a[i]] = i
    else:
        d = a[i]
        l, r = res[d], n-i


def cmb(n, r, mod):
    if (r < 0 or r > n):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]

for i in range(2, n + 2):
    g1.append((g1[-1] * i) % mod)
    inverse.append((-inverse[mod % i] * (mod//i)) % mod)
    g2.append((g2[-1] * inverse[-1]) % mod)


for i in range(1, n+2):
    print((cmb(n+1, i, mod)-cmb(l+r, i-1, mod)) % mod)

Solution (Python):
class PERM_COMB_MOD():
    
    def __init__(self, max_n=510000, mod=10**9+7):
        self.fac = [0]*max_n
        self.finv = [0]*max_n
        self.inv = [0]*max_n
        self.fac[0] = self.fac[1] = 1
        self.finv[0] = self.finv[1] = 1
        self.inv[1] = 1
        self.max = max_n
        self.mod = mod
        self._maesyori()

    def _maesyori(self):
        for i in range(2,self.max):
            self.fac[i] = self.fac[i-1] * i % self.mod
            self.inv[i] = self.mod - self.inv[self.mod % i] * (self.mod // i) % self.mod
            self.finv[i] = self.finv[i-1] * self.inv[i] % self.mod

    def comb(self, n, k):
        if n < k : return 0
        if n < 0 or k < 0:return 0
        return self.fac[n] * (self.finv[k] * self.finv[n-k] % self.mod) % self.mod

mod = 10**9+7

n = int(input())
p = PERM_COMB_MOD(n+10)
a = list(map(int, input().split()))
d = {}
l=r=None

for i, ai in enumerate(a):
    if ai in d:
        l = d[ai]
        r = i
        break
    else:
        d[ai] = i

s = l+n-r

for k in range(n+1):
    ans = p.comb(n+1, k+1) - p.comb(s, k)
    print(ans%mod)

Solution (Python):
m=10**9+7
n=int(input())
a=list(map(int,input().split()))
b=[0]*(n+1)
for i in range(n+1):
    if b[a[i]]==0:
        b[a[i]]=i+1
    else:
        s=b[a[i]]+n-i-1
        break
p,q=1,1
for i in range(1,n+2):
    p=((p*(n+2-i))*pow(i,m-2,m))%m
    q=(1 if i==1 and s>=i-1 else(0 if s<i-1 else ((q*(s-i+2))*pow(i-1,m-2,m)))%m)
    print((p-q)%m)

Solution (Python):
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
from operator import mul
from functools import reduce


INF = float('inf')
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return sys.stdin.readline().strip()
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 1000000007


n = I() + 1
A = LI()
D = defaultdict(lambda:-1)
for i in range(n):
    if D[A[i]] != -1:
        l = D[A[i]]
        r = n - i - 1
        break
    else:
        D[A[i]] = i


fac = [1] * (n + 1)
inv = [1] * (n + 1)
i = 1
for j in range(1, n + 1):
    i = i * j % mod
    fac[j] = i
    inv[j] = pow(i, mod - 2, mod)



def comb(n, r):
    if r > n or n < 0 or r < 0:
        return 0
    return fac[n] * inv[n - r] * inv[r] % mod


for j in range(1, n + 1):
    print((comb(n, j) - comb(r + l, j - 1)) % mod)

Solution (Python):
n=int(input())
a=[int(j) for j in input().split()]
mod=10**9+7
l=[-1]*(n+1)
ind=[]
for i in range(n+1):
    if l[a[i]]!=-1:
        ind=[l[a[i]],i]
        break
    l[a[i]]=i
U = 2*10**5
MOD = 10**9+7
 
fact = [1]*(U+1)
fact_inv = [1]*(U+1)
 
for i in range(1,U+1):
  fact[i] = (fact[i-1]*i)%MOD
fact_inv[U] = pow(fact[U],MOD-2,MOD)
 
for i in range(U,0,-1):
	fact_inv[i-1] = (fact_inv[i]*i)%MOD
 
def comb(n,k):
  if k < 0 or k > n:
    return 0
  x = fact[n]
  x *= fact_inv[k]
  x %= MOD
  x *= fact_inv[n-k]
  x %= MOD
  return x

i,j=ind
for k in range(1,n+2):
    if k==1:
        print(n)
    else:
        print((comb(n+1,k)-comb(i+n-j,k-1))%mod)

Solution (Python):
import sys
input = sys.stdin.readline

N = int(input())
A = list(map(int, input().split()))

mod = int(10**9+7) 

def cmb(n, r, mod=mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

NN = 5*10**5 
g1 = [1, 1] 
g2 = [1, 1] 
inverse = [0, 1] 

for i in range( 2, NN + 1 ):
    g1.append( ( g1[-1] * i ) % mod )
    inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )


dic = {}
for i, a in enumerate(A):
    if not a in dic.keys():
        dic[a] = i
    else:
        l, r = dic[a], i
        break

ans = [0]*(N+2)

for k in range(N):
    nCk = cmb(N-1, k)
    ans[k] = (ans[k] + nCk) % mod
    ans[k+1] = (ans[k+1] + 2*nCk - cmb(N-r+l, k)) % mod
    ans[k+2] = (ans[k+2] + nCk) % mod

for k in range(1, N+2):
    print(ans[k])