#include #include #include #include #include #include #include #include #include #include #include #include #include #define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl; #define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } using namespace std; typedef long long ll; template vector> vec2d(int n, int m, T v){ return vector>(n, vector(m, v)); } template vector>> vec3d(int n, int m, int k, T v){ return vector>>(n, vector>(m, vector(k, v))); } template void print_vector(vector v, char delimiter=' '){ if(v.empty()) { cout << endl; return; } for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter; cout << v.back() << endl; } const ll MOD = 1000000007; class ModInt{ public: ll v; ModInt(ll _v = 0){ if(_v < 0) _v = (_v%MOD)+MOD; if(_v >= MOD) _v %= MOD; v = _v; } ModInt operator+(ll n){ return ModInt((v+n)%MOD); } ModInt operator-(ll n){ return ModInt((v-n+MOD)%MOD); } ModInt operator*(ll n){ if(n >= MOD) n %= MOD; return ModInt((v*n)%MOD); } ModInt operator/(ll n){ return ModInt((ModInt(n).inv()*v).v%MOD); } void operator+=(ll n){ v = (v+n)%MOD; } void operator-=(ll n){ v = (v-n+MOD)%MOD; } void operator*=(ll n){ v = (v*n+MOD)%MOD; } ModInt operator+(ModInt n){ return ModInt((v+n.v)%MOD); } ModInt operator-(ModInt n){ return ModInt((v-n.v+MOD)%MOD); } ModInt operator*(ModInt n){ return ModInt((v*n.v)%MOD); } ModInt operator/(ModInt n){ return ModInt((n.inv()*v).v%MOD); } void operator+=(ModInt n){ v = (v+n.v)%MOD; } void operator-=(ModInt n){ v = (v-n.v+MOD)%MOD; } void operator*=(ModInt n){ v = (v*n.v)%MOD; } void operator=(ModInt n){ v = n.v; } bool operator==(ModInt n){ return v == n.v; } bool operator!=(ModInt n){ return v != n.v; } void operator=(ll n){ v = n%MOD; } ModInt inv(){ if(v == 1) return ModInt(1); else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD); } }; ostream& operator<<(ostream& os, const ModInt& m){ os << m.v; return os; } istream & operator >> (istream &in, ModInt &m){ in >> m.v; return in; } template class Compress{ public: vector data; int offset; Compress(vector data_, int offset=0): offset(offset){ set st; for(T x: data_) st.insert(x); for(T x: st) data.push_back(x); }; int operator[](T x) { auto p = lower_bound(data.begin(), data.end(), x); assert(x == *p); return offset+(p-data.begin()); } T inv(int x){ return data[x-offset]; } int size(){ return data.size(); } }; vector facs(ll n){ vector ans; for(int i = 1; i*i <= n ; i++){ if(n%i == 0){ ans.push_back(i); if(i*i != n) ans.push_back(n/i); } } sort(ans.begin(), ans.end()); return ans; } using mint = ModInt; int main(){ ios::sync_with_stdio(false); cin.tie(0); cout << setprecision(10) << fixed; int n; ll k; cin >> n >> k; vector a(n); for(int i = 0; i < n; i++) cin >> a[i]; auto f = facs(k); auto cp = Compress(f); int m = cp.size(); auto dp = vec2d(n+1, m+1, mint(0)); dp[0][cp[1]] = 1; for(int i = 0; i < n; i++){ ll g = gcd(a[i], k); for(int j = 0; j < m; j++){ ll cur = cp.data[j]; ll nx = gcd(k, g*cur); dp[i+1][cp[nx]] += dp[i][j]; dp[i+1][j] += dp[i][j]; // debug_value(nx); } } cout << dp[n][cp[k]] << endl; }