#include using namespace std; #define repd(i,a,b) for (ll i=(a);i<(b);i++) #define rep(i,n) repd(i,0,n) #define all(x) (x).begin(),(x).end() template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } typedef long long ll; typedef pair P; typedef vector vec; typedef vector Graph; const long long INF = 1LL<<60; const long long MOD = 1000000007; // auto mod int // https://youtu.be/L8grWxBlIZ4?t=9858 // https://youtu.be/ERZuLAxZffQ?t=4807 : optimize // https://youtu.be/8uowVvQ_-Mo?t=1329 : division const int mod = 998244353; struct mint { ll x; // typedef long long ll; 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, mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} // Sieve of Eratosthenes // https://youtu.be/UTVg7wzMWQc?t=2774 struct Sieve { int n; vector f, primes; Sieve(int n=1):n(n), f(n+1) { f[0] = f[1] = -1; for (ll i = 2; i <= n; ++i) { if (f[i]) continue; primes.push_back(i); f[i] = i; for (ll j = i*i; j <= n; j += i) { if (!f[j]) f[j] = i; } } } bool isPrime(int x) { return f[x] == x;} vector factorList(int x) { vector res; while (x != 1) { res.push_back(f[x]); x /= f[x]; } return res; } vector

factor(int x) { vector fl = factorList(x); if (fl.size() == 0) return {}; vector

res(1, P(fl[0], 0)); for (int p : fl) { if (res.back().first == p) { res.back().second++; } else { res.emplace_back(p, 1); } } return res; } vector> factor(ll x) { vector> res; for (int p : primes) { int y = 0; while (x%p == 0) x /= p, ++y; if (y != 0) res.emplace_back(p,y); } if (x != 1) res.emplace_back(x,1); return res; } }sieve(100000); int main() { ios::sync_with_stdio(false); cin.tie(0); ll n,m;cin>>n>>m; vec a(n); rep(i,n)cin>>a[i]; ll l=a[0]; repd(i,1,n){ ll memo=gcd(l,a[i]); l=l*a[i]/memo; } mint ans=0; auto memo=sieve.factor(l); auto f=[&](ll x){ ll cnt=0; rep(i,n){ ll g=gcd(x,a[i]); cnt+=g; } mint add=mint(m).pow(cnt); mint now=l/x; ll c=l/x; for(auto[u,v]:memo){ if(c%u==0){ now*=(u-1); now/=u; } } add*=now; ans+=add; }; for(ll i=1;i*i<=l;i++){ if(l%i)continue; f(i); if(i*i!=l)f(l/i); } ans/=l; cout<