p03674 AtCoder Beginner Contest 066 - 11
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.

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.

Examples

Input

3
1 2 1 3


Output

3
5
4
1


Input

1
1 1


Output

1
1


Input

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


Output

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
```python
# ------ combination -------
N, MOD = 10**5 + 1, 10**9 + 7
fc, ifc = [0] * (N+1), [0] * (N+1)

def power(n, a):
    res, exp = 1, n
    while(a):
        if a & 1:
            res = res * exp % MOD
        exp = exp * exp % MOD
        a = a >> 1
    return res

fc[0] = 1
for i in range(1, N+1):
    fc[i] = fc[i-1] * i % MOD
ifc[N] = power(fc[N], MOD-2)
for i in range(N-1, -1, -1):
    ifc[i] = ifc[i+1] * (i+1) % MOD

def Comb(n, r):
    if n < 0 or r < 0 or n < r:
        return 0
    return fc[n] * ifc[r] % MOD * ifc[n-r] % MOD

# --------------------------

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

num = [-1] * (n+1)
l = r = -1
for i in range(len(a)):
    if num[a[i]] != -1:
        l, r = num[a[i]], i
        break
    num[a[i]] = i

for k in range(1, len(a)+1):
    ans = Comb(len(a), k) - Comb(l+len(a)-r-1, k-1)
    while ans < 0:
        ans += MOD
    print(ans)
```