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 in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,s,n) for(int i=(s);i<=(n);i++)
#define repr(i,n) for(int i=n-1;i>=0;i--)
#define REPR(i,s,n) for(int i=(s);i>=(n);i--)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define Eunique(v) v.erase(unique(all(v)),v.end())
#define Eback(s) s.erase(s.end()-1,s.end())
#define rev(v) reverse(all(v))
#define minvec(v) *min_element(all(v))
#define maxvec(v) *max_element(all(v))
#define sumvec(v) accumulate(all(v),0LL)
#define mapmin(v) v.rbegin()->first
#define mapmax(v) v.begin()->first
#define pb push_back
#define pf push_front
#define m_p make_pair
#define DOUBLE fixed << setprecision(15)
#define OK cerr<<"OK\n"
#define OK1 cerr<<"OK1\n"
#define OK2 cerr<<"OK2\n"
#define sz(s) (long long)s.size()
#define INF ((1LL<<62)-(1LL<<31))
#define zero(x,n) setw(x) << setfill('0') << n
#define endl '\n'

typedef long long ll;

typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<long long> vll;
typedef vector<vll> vvll;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<string> vs;

typedef pair<ll,ll> pll;
typedef pair<int,int> pii;
typedef vector<pair<int,int>> vpii;
typedef vector<pair<ll,ll>> vpll;

const double pi = acos(-1.0);
const ll mod=1000000007;
const ll mod2=998244353;

template<class A, class B>
ostream& operator<<(ostream& ost, const pair<A, B>&p) {
	ost << "{" << p.first << ", " << p.second << "} ";
	return ost;
}

template<class T>
ostream& operator<<(ostream& ost, const vector<T>&v) {
	ost << "{";
	for (int i = 0; i<(int)v.size(); i++) {
		if (i)ost << " ";
		ost << v[i];
	}
	ost << "} \n";
	return ost;
}

template<class A, class B>
ostream& operator<<(ostream& ost, const map<A, B>&v) {
	ost << "{";
	for (auto p:v) {
		ost << "{" << p.first << ", " << p.second << "} ";
	}
	ost << "} ";
	return ost;
}

void out(){cout << "\n";}
template<class T,class... Args>
void out(const T &x,const Args &... args){
	cout << x << " ";
	out(args...);
}

template<typename T>
istream& operator >> (istream& is, vector<T>& vec){
	for(T& e: vec) is >> e;
	return is;
}

template<typename T>
string join(vector<T>& vec, string sep=" "){
	stringstream ss;
	for(int i=0;i<(int)vec.size();i++){
		ss << vec[i] << (i+1==(int)vec.size()?"\n":sep);
	}
	return ss.str();
}

template<class T>
inline bool chmax(T& a, T b){if(a<b){a=b;return true;} return false;}

template<class T>
inline bool chmin(T& a, T b){if(a>b){a=b;return true;} return false;}

void YES(bool b) {cout << ((b)?"YES\n":"NO\n");}
void Yes(bool b) {cout << ((b)?"Yes\n":"No\n");}
void yes(bool b) {cout << ((b)?"yes\n":"no\n");}
void Yay(bool b) {cout << ((b)?"Yay!\n":":(\n");}

ll powmod(ll a,ll b){ll c=1; while(b>0){ if(b&1){ c=a*c%mod; } a=a*a%mod; b>>=1; } return c;}
ll nCrmod(ll n,ll r){ll x=1,y=1; for(ll i=0;i<r;i++) {x=x*(n-i)%mod; y=y*(i+1)%mod; } return x*powmod(y,mod-2)%mod;}
ll gcd(ll x, ll y) {return __gcd(x,y);}
ll lcm(ll x, ll y) {return x/__gcd(x,y)*y;}

struct mint {
    ll x;
    mint(ll x=0):x((x%mod+mod)%mod) {}
    mint operator-() const {return mint(-x);}
    mint& operator+=(const mint a) {
        if((x+=a.x)>=mod) x-=mod;
        return *this;
    }
    mint& operator-=(const mint a) {
        if((x+=mod-a.x)>=mod) x-=mod;
        return *this;
    }
    mint& operator*=(const mint a) {(x*=a.x)%=mod; return *this;}
    mint operator+(const mint a) const {return mint(*this)+=a;}
    mint operator-(const mint a) const {return mint(*this)-=a;}
    mint operator*(const mint a) const {return mint(*this)*=a;}
    mint pow(ll t) const {
        if(!t) return 1;
        mint a=pow(t>>1);
        a*=a;
        if(t&1) a*=*this;
        return a;
    }

    //for prime mod
    mint inv() const {return pow(mod-2);}
    mint& operator/=(const mint a) {return *this*=a.inv();}
    mint operator/(const mint a) const {return mint(*this)/=a;}
};
istream& operator>>(istream& is, const mint& a) {return is>>a.x;}
ostream& operator<<(ostream& os, const mint& a) {return os<<a.x;}

//combination mod prime
//with mint
struct combination{
    vector<mint> fact,ifact;
    combination(int n):fact(n+1),ifact(n+1){
        assert(n<mod);
        fact[0]=1;
        for(int i=1;i<=n;i++) fact[i]=fact[i-1]*i;
        ifact[n]=fact[n].inv();
        for(int i=n;i>=1;i--) ifact[i-1]=ifact[i]*i;
    }
    mint operator()(int n,int k){
        if(k<0 || n<k) return 0;
        return fact[n]*ifact[k]*ifact[n-k];
    }
};

int main()
{
	ll n;
	cin >> n;
	vll a(n+1);
	map<ll,ll> m;
	ll two=0;
	rep(i,n+1){
		cin >> a[i];
		m[a[i]]++;
		if(m[a[i]]==2) two=a[i];
	}
	ll l=-1,r=-1;
	rep(i,n+1){
		if(a[i]==two){
			if(l==-1) l=i;
			else r=i;
		}
	}
	combination c(n+5);
	for(ll i=1;i<=n+1;i++){
		mint ans=c(n+1,i)-c(l+n-r,i-1);
		cout << ans.x << endl;
	}
	return 0;
}