#include using namespace std; using ll = long long; using ull = unsigned long long; using i128 = __int128_t; using pii = pair; using pll = pair; template using vec = vector; template using vvec = vector>; #define rep(i, n) for (int i = 0; i < (n); i++) #define rrep(i, n) for (int i = int(n) - 1; i >= 0; i--) #define all(x) (x).begin(), (x).end() constexpr char ln = '\n'; template inline int SZ(Container& v) { return int(v.size()); } template inline void UNIQUE(vector& v) { v.erase(unique(v.begin(), v.end()), v.end()); } template inline bool chmax(T1& a, T2 b) { if (a < b) {a = b; return true ;} return false ;} template inline bool chmin(T1& a, T2 b) { if (a > b) {a = b; return true ;} return false ;} inline int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); } inline int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); } inline int popcount(ull x) { return __builtin_popcountll(x); } inline int kthbit(ull x, int k) { return (x>>k) & 1; } inline constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x-1) * 10; } struct fast_ios { fast_ios() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// //O(NloglogN) で約数・倍数の畳み込み // (1) divisor_zeta : 倍数方向に高速ゼータ変換(累積和) // (2) divisor_moebius : 約数方向に高速メビウス変換(包除原理) (1)の逆 // (3) multiple_zeta : 約数方向に高速ゼータ変換(累積和) // (4) multiple_moebius : 倍数方向に高速メビウス変換(包除原理) (3)の逆 // メビウス関数は c[1] = 1 として(2) で求まる struct PrimeZeta { int n_; vector sieve; PrimeZeta() {} PrimeZeta(int n) : n_(n), sieve(n+1, true) { sieve[0] = sieve[1] = false; for (int i = 2; i*i <= n; i++) { if (sieve[i]) { for (int j = i*i; j <= n; j += i) { sieve[j] = false; } } } } // (1) divisor_zeta : 倍数方向に高速ゼータ変換(累積和) template void divisor_zeta(T &c) { int n = int(c.size()); assert(n-1 <= n_); for (int i = 2; i < n; i++) { if (sieve[i]) { for (int j = 1; j*i < n; j++) { c[j*i] += c[j]; } } } } // (2) divisor_moebius : 約数方向に高速メビウス変換(包除原理) (1)の逆 template void divisor_moebius(T &c) { int n = int(c.size()); assert(n-1 <= n_); for (int i = 2; i < n; i++) { if (sieve[i]) { for (int j = (n-1)/i; j >= 1; j--) { c[j*i] -= c[j]; } } } } // (3) multiple_zeta : 約数方向に高速ゼータ変換(累積和) template void multiple_zeta(T &c) { int n = int(c.size()); assert(n-1 <= n_); for (int i = 2; i < n; i++) { if (sieve[i]) { for (int j = (n-1)/i; j >= 1; j--) { c[j] += c[j*i]; } } } } // (4) multiple_moebius : 倍数方向に高速メビウス変換(包除原理) (3)の逆 template void multiple_moebius(T &c) { int n = int(c.size()); assert(n-1 <= n_); for (int i = 2; i < n; i++) { if (sieve[i]) { for (int j = 1; j*i < n; j++) { c[j] -= c[j*i]; } } } } }; ////////////////////////////////////////////////////////////////////////////////////////////////////// template struct ModInt { public: static constexpr int mod() { return m; } static ModInt raw(int v) { ModInt x; x._v = v; return x; } ModInt() : _v(0) {} ModInt(long long v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } unsigned int val() const { return _v; } ModInt& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } ModInt& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } ModInt operator++(int) { ModInt result = *this; ++*this; return result; } ModInt operator--(int) { ModInt result = *this; --*this; return result; } ModInt& operator+=(const ModInt& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } ModInt& operator-=(const ModInt& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } ModInt& operator*=(const ModInt& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } ModInt& operator^=(long long n) { ModInt x = *this; *this = 1; if (n < 0) x = x.inv(), n = -n; while (n) { if (n & 1) *this *= x; x *= x; n >>= 1; } return *this; } ModInt& operator/=(const ModInt& rhs) { return *this = *this * rhs.inv(); } ModInt operator+() const { return *this; } ModInt operator-() const { return ModInt() - *this; } ModInt pow(long long n) const { ModInt r = *this; r ^= n; return r; } ModInt inv() const { int a = _v, b = umod(), y = 1, z = 0, t; for (; ; ) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1); return ModInt(b * z); } y -= t * z; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1); return ModInt(a * y); } z -= t * y; } } friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) += rhs; } friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) -= rhs; } friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) *= rhs; } friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) /= rhs; } friend ModInt operator^(const ModInt& lhs, long long rhs) { return ModInt(lhs) ^= rhs; } friend bool operator==(const ModInt& lhs, const ModInt& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const ModInt& lhs, const ModInt& rhs) { return lhs._v != rhs._v; } friend ModInt operator+(long long lhs, const ModInt& rhs) { return (ModInt(lhs) += rhs); } friend ModInt operator-(long long lhs, const ModInt& rhs) { return (ModInt(lhs) -= rhs); } friend ModInt operator*(long long lhs, const ModInt& rhs) { return (ModInt(lhs) *= rhs); } friend ostream& operator<<(ostream& os, const ModInt& M) { return os << M._v; } friend istream& operator>>(istream& is, ModInt& M) { long long x; is >> x; M = ModInt(x); return is; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } }; constexpr int MOD = 1000000007; //constexpr int MOD = 998244353; using mint = ModInt; struct ModCombination { private: int max_n; vector fac_,facinv_; public: ModCombination() {} ModCombination(int n) : max_n(n), fac_(n+1), facinv_(n+1) { assert(1 <= n); fac_[0] = 1; for (int i = 1; i <= n; i++) fac_[i] = fac_[i-1]*i; facinv_[n] = fac_[n].inv(); for (int i = n; i >= 1; i--) facinv_[i-1] = facinv_[i]*i; } mint fac(int k) const { assert(0 <= k and k <= max_n); return fac_[k]; } mint facinv(int k) const { assert(0 <= k and k <= max_n); return facinv_[k]; } mint invs(int k) const { assert(1 <= k and k <= max_n); return facinv_[k]*fac_[k-1]; } mint P(int n, int k) const { if (k < 0 or k > n) return mint(0); assert(n <= max_n); return fac_[n]*facinv_[n-k]; } mint C(int n, int k) const { if (k < 0 or k > n) return mint(0); assert(n <= max_n); return fac_[n]*facinv_[n-k]*facinv_[k]; } mint H(int n, int k) const { if (n == 0 and k == 0) return mint(1); return C(n+k-1,k); } mint catalan(int n) const { if (n == 0) return mint(1); return C(n*2,n) - C(n*2,n-1); } }; //O(NloglogN) struct PrimeFactorTable { int n; vector table; PrimeFactorTable() {} PrimeFactorTable(int n_) : n(n_), table(n_+1) { iota(table.begin(),table.end(),0); for (int i = 2; i*i <= n; i++) { if (table[i] == i) { for (int j = i*i; j <= n; j += i) { if (table[j] == j) table[j] = i; } } } } int operator[](int x) const { return table[x]; } vector> prime_factor(int x) { assert(1 <= x and x <= n); vector> ret; while (x != 1) { if (ret.empty() or ret.back().first != table[x]) { ret.emplace_back(table[x],1); } else { ret.back().second++; } x /= table[x]; } return ret; } }; void yukico886() { int H,W; cin >> H >> W; const int MAX = 3e6; PrimeZeta zet(MAX); vec cnt(MAX+1); for (int i = 1; i < H; i++) { cnt[i] = H-i; } zet.multiple_zeta(cnt); vec e(MAX+1); e[1] = 1; zet.divisor_moebius(e); rep(i,MAX+1) { cnt[i] *= e[i]; } zet.divisor_zeta(cnt); mint ans = 0; for (int i = 1; i < W; i++) { ans += cnt[i]*(W-i); } ans *= 2; ans += mint(H)*(W-1) + mint(W)*(H-1); cout << ans << ln; } void CF325E() { const int MAX = 1e7; PrimeFactorTable PFT(MAX); PrimeZeta PZ(MAX); int N; cin >> N; vec A(N),divs(MAX+1); rep(i,N) { cin >> A[i]; divs[A[i]]++; } vec beki(N+1,1); rep(i,N) beki[i+1] = beki[i]*2; PZ.multiple_zeta(divs); vec S(MAX+1); rep(i,MAX+1) S[i] = beki[divs[i]] - 1; PZ.multiple_moebius(S); S[1] = 0; PZ.multiple_zeta(S); mint ans = 0; rep(i,N) { auto primes = PFT.prime_factor(A[i]); int K = primes.size(); mint tmp = 0; rep(mask,1<