#ifdef MAIN bool __multi__ = 0; using INT = long long; namespace XK { const INT mod = 1e9 + 7; vector divisor(ull x){ vector ans; for(ull i = 1; i * i <= x; i++) if(x % i == 0) ans.push_back(i); rrep(i, 0, ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]); return ans; } void solve() { INT N, K; cin >> N >> K; V A(N); rep(i, N) cin >> A[i], A[i] = gcd(A[i], K); auto div = divisor(K); // div.pb(K); #ifdef DEBUG rep(i, sz(div)) cout << div[i] << " \n"[i == sz(div) - 1]; #endif unordered_map f; rep(i, sz(div)) f[i] = 0; f[1] = 1; rep(i, N) { unordered_map nf; rep(j, sz(div)) { (nf[div[j]] += f[div[j]]) %= mod; (nf[gcd(K, A[i] * div[j])] += f[div[j]]) %= mod; } #ifdef DEBUG cout << i << " : "; for(auto [x, y] : nf) cout << "[" << x << ": " << y<< "]" << ","; cout << '\n'; #endif swap(f, nf); } cout << (f[K] - (K == 1) + mod) % mod; } }; #else #include "cassert" #include "cmath" #include "cstdint" #include "cstdio" #include "cstdlib" #include "cstring" #include "algorithm" #include "bitset" #include "chrono" #include "complex" #include "deque" #include "functional" #include "iostream" #include "limits" #include "map" #include "numeric" #include "queue" #include "random" #include "set" #include "sstream" #include "string" #include "unordered_map" #include "unordered_set" #include "utility" #include "vector" #include "array" using namespace std; #define int long long using ll = long long; using ull = unsigned long long; const ll INF = 1ll << 60; const ll LINF = 0x1fffffffffffffff; const ll MINF = 0x7fffffffffff; template bool chmax(A& l, const B& r){ return r > l ? l = r, 1 : 0; } template bool chmin(A& l, const B& r){ return r < l ? l = r, 1 : 0; } #define sz(x) ssize(x) #define rep(i, a) for(ll i = 0; i < (a); i ++) #define Rep(i, a, b) for(ll i = (a); i < (b); i ++) #define rrep(i, a, b) for(ll i = (b); i --> (a); ) #define all(x) begin(x), end(x) #define fst first #define snd second #define pb push_back template using V = vector; template using AR = array; #define MAIN #include __FILE__ signed main() {ios::sync_with_stdio(0);cin.tie(0);fixed(cout).precision(12);int t = 1;if(__multi__) cin >> t;while(t --) XK::solve();} #endif