Problem:
Score : 600 points

Problem Statement

Snuke has a blackboard and a set S consisting of N integers.
The i-th element in S is S_i.

He wrote an integer X on the blackboard, then performed the following operation N times:

Choose one element from S and remove it.

Let x be the number written on the blackboard now, and y be the integer removed from S. Replace the number on the blackboard with x \bmod {y}.

There are N! possible orders in which the elements are removed from S.
For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.

Constraints

All values in input are integers.

1 \leq N \leq 200

1 \leq S_i, X \leq 10^{5}

S_i are pairwise distinct.

Input

Input is given from Standard Input in the following format:

N X
S_1 S_2 \ldots S_{N}

Output

Print the answer.

Sample Input 1

2 19
3 7

Sample Output 1

3

There are two possible orders in which we remove the numbers from S.

If we remove 3 and 7 in this order, the number on the blackboard changes as follows: 19 \rightarrow 1 \rightarrow 1.

If we remove 7 and 3 in this order, the number on the blackboard changes as follows: 19 \rightarrow 5 \rightarrow 2.

The output should be the sum of these: 3.

Sample Input 2

5 82
22 11 6 5 13

Sample Output 2

288

Sample Input 3

10 100000
50000 50001 50002 50003 50004 50005 50006 50007 50008 50009

Sample Output 3

279669259

Be sure to compute the sum modulo 10^{9}+7.

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using ld=long double;
using ull=unsigned long long;
using uint=unsigned int;
using pcc=pair<char,char>;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using pdd=pair<double,double>;
using tuplis=pair<ll,pll>;
using tuplis2=pair<pll,ll>;
template<class T> using pq=priority_queue<T,vector<T>,greater<T>>;
const ll LINF=0x1fffffffffffffff;
const ll MOD=1000000007;
const ll MODD=998244353;
const int INF=0x3fffffff;
const double DINF=numeric_limits<double>::infinity();
const vector<pii> four={{-1,0},{0,1},{1,0},{0,-1}};
#define _overload4(_1,_2,_3,_4,name,...) name
#define _overload3(_1,_2,_3,name,...) name
#define _rep1(n) for(ll i=0;i<n;++i)
#define _rep2(i,n) for(ll i=0;i<n;++i)
#define _rep3(i,a,b) for(ll i=a;i<b;++i)
#define _rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) _overload4(__VA_ARGS__,_rep4,_rep3,_rep2,_rep1)(__VA_ARGS__)
#define _rrep1(n) for(ll i=n-1;i>=0;i--)
#define _rrep2(i,n) for(ll i=n-1;i>=0;i--)
#define _rrep3(i,a,b) for(ll i=b-1;i>=a;i--)
#define _rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c)
#define rrep(...) _overload4(__VA_ARGS__,_rrep4,_rrep3,_rrep2,_rrep1)(__VA_ARGS__)
#define each(i,a) for(auto& i:a)
#define sum(...) accumulate(range(__VA_ARGS__),0LL)
#define dsum(...) accumulate(range(__VA_ARGS__),double(0))
#define _range(i) (i).begin(),(i).end()
#define _range2(i,k) (i).begin(),(i).begin()+k
#define _range3(i,a,b) (i).begin()+a,(i).begin()+b
#define range(...) _overload3(__VA_ARGS__,_range3,_range2,_range)(__VA_ARGS__)
#define _rrange(i) (i).rbegin(),(i).rend()
#define _rrange2(i,k) (i).rbegin(),(i).rbegin()+k
#define _rrange3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rrange(...) _overload3(__VA_ARGS__,_rrange3,_rrange2,_rrange)(__VA_ARGS__)
#define yes(i) out(i?"yes":"no")
#define Yes(i) out(i?"Yes":"No")
#define YES(i) out(i?"YES":"NO")
#define Possible(i) out(i?"Possible":"Impossible")
#define elif else if
#define unless(a) if(!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define vec(type,name,...) vector<type> name(__VA_ARGS__)
#define VEC(type,name,size) vector<type> name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
__attribute__((constructor)) void SETTINGS(){cin.tie(0); cout.tie(0); ios::sync_with_stdio(0); cout<<fixed<<setprecision(20);};
inline constexpr ll gcd(ll a,ll b){if(!a||!b)return 0;if(a<b){ll c=a;a=b;b=c;}while(b){ll c=b;b=a%b;a=c;}return a;}
inline constexpr ll lcm(ll a,ll b){if(!a||!b)return 0;return a*b/gcd(a,b);}
template<class T>inline constexpr T min(vector<T>& v){return *min_element(range(v));}
inline char min(string& v){return *min_element(range(v));}
template<class T>inline constexpr T max(vector<T>& v){return *max_element(range(v));}
inline char max(string& v){return *max_element(range(v));}
inline constexpr ll intpow(const ll&a,const ll&b){if(b==0)return 1;ll ans=intpow(a,b/2);return ans*ans*(b&1?a:1);}
inline constexpr ll modpow(const ll&a,const ll&b,const ll&mod=MOD){if(b==0)return 1;ll ans=modpow(a,b/2,mod);ans=ans*ans%mod;if(b&1)ans=ans*a%mod;return ans;}
template<typename T>
inline constexpr bool update_min(T& mn,const T& cnt){if(mn>cnt){mn=cnt;return 1;}else return 0;}
template<typename T>
inline constexpr bool update_max(T& mx,const T& cnt){if(mx<cnt){mx=cnt;return 1;}else return 0;}
inline void in() {}
template<class T>
istream& operator >> (istream& is, vector<T>& vec);
template<class T,size_t size>
istream& operator >> (istream& is, array<T,size>& vec);
template<class T,class L>
istream& operator >> (istream& is, pair<T,L>& p);
template<class T>
ostream& operator << (ostream& os, vector<T>& vec);
template<class T,class L>
ostream& operator << (ostream& os, pair<T,L>& p);
template<class T>
istream& operator >> (istream& is, vector<T>& vec){for(T& x: vec) is >> x;return is;}
template<class T,class L>
istream& operator >> (istream& is, pair<T,L>& p){is >> p.first;is >> p.second;return is;}
template<class T>
ostream& operator << (ostream& os, vector<T>& vec){os << vec[0];rep(i,1,vec.size()){os << ' ' << vec[i];}return os;}
template<class T>
ostream& operator << (ostream& os, deque<T>& deq){os << deq[0];rep(i,1,deq.size()){os << ' ' << deq[i];}return os;}
template<class T,class L>
ostream& operator << (ostream& os, pair<T,L>& p){os << p.first << " " << p.second;return os;}
template<class T,class L>
pair<T,L> operator + (pair<T,L> a, pair<T,L> b){return {a.first + b.first, a.second + b.second};}
template <class Head, class... Tail>
inline void in(Head&& head,Tail&&... tail){cin>>head;in(move(tail)...);}
template <class T>
inline bool out(T t){cout<<t<<'\n';return 0;}
inline bool out(){cout<<'\n';return 0;}
template <class Head, class... Tail>
inline bool out(Head head,Tail... tail){cout<<head<<' ';out(move(tail)...);return 0;}
template <class T>
inline void err(T t){cerr<<t<<'\n';}
inline void err(){cerr<<'\n';}
template <class Head, class... Tail>
inline void err(Head head,Tail... tail){cerr<<head<<' ';out(move(tail)...);}



const ll mod = MOD;
ll extgcd(ll a, ll b, ll &x, ll &y){ ll g = a; x = 1; y = 0; if(b){ g = extgcd(b, a % b, y, x); y -= a / b * x; } return g; }
ll invmod(ll a, ll m = mod){ ll x, y; extgcd(a, m, x, y); return (x + m) % m; }
struct Modint{
    ll _num;
    Modint(){ _num = 0; }
    Modint(ll x){ _num = x % mod; if(_num < 0) _num += mod; }
    Modint operator= (ll x){ _num=x%mod; if(_num<0)_num+=mod; return *this; }
    Modint operator+ (ll x){ return Modint(_num + x); }
    Modint operator- (ll x){ return Modint(_num - x); }
    Modint operator* (ll x){ return Modint(_num * (x % mod)); }
    Modint operator+=(ll x){ _num += x; _num %= mod; if(_num < 0) _num += mod; return *this; }
    Modint operator-=(ll x){ _num -= x; _num %= mod; if(_num < 0) _num += mod; return *this; }
    Modint operator*=(ll x){ x %= mod; _num *= x; _num %= mod; if(_num < 0) _num += mod; return *this; }
    Modint operator/ (ll x){ return Modint(_num * invmod(x % mod, mod)); }
    Modint operator/= (ll x){ _num *= invmod(x % mod, mod); _num %= mod; if(_num < 0) _num += mod; return *this; }
    Modint pow(ll x){ ll i = 1; Modint ans = 1, cnt = *this; while(i <= x){ if(x & i){ ans *= cnt; x ^= i; } cnt *= cnt; i *= 2; } return ans; }
    operator ll() const { return _num; }
};
vector<Modint>fac{1},inv{1};
void reserve(ll a){
    if(fac.size() >= a) return;
    update_max(a, ll(fac.size()) * 2);
    while(fac.size() < a) fac.push_back(fac.back() * ll(fac.size()));
    inv.resize(fac.size());
    inv.back() = Modint(1) / fac.back();
    for(ll i = inv.size() - 1; !inv[i - 1]; i--) inv[i - 1] = inv[i] * i;
}
Modint perm(ll n, ll r){ reserve(n + 1); return fac[n] * inv[n - r]; }
Modint comb(ll n, ll r){ reserve(n + 1); return fac[n] * inv[r] * inv[n - r]; }
Modint Mcomb(ll n, ll r){ return comb(n + r - 1, n - 1); } // r個をn部屋に分ける
vector<ll>s;
Modint dp(ll at,ll p){
    if(!at)return p%s[0];
    Modint ans=0;
    rep(at)ans+=dp(i,p%s[at])*perm(at-1,at-i-1);
    return ans;
}
signed main(){
    LL(n,x);
    s.resize(n);
    reserve(n+1);
    in(s);
    sort(range(s));
    s.push_back(LINF);
    out(dp(n,x));
}