#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using P = pair; constexpr int INF = 1001001001; constexpr int mod = 1000000007; // constexpr int mod = 998244353; template inline bool chmax(T& x, T y){ if(x < y){ x = y; return true; } return false; } template inline bool chmin(T& x, T y){ if(x > y){ x = y; return true; } return false; } struct mint { int x; mint() : x(0) {} mint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} mint& operator+=(const mint& p){ if((x += p.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint& p){ if((x -= p.x) < 0) x += mod; return *this; } mint& operator*=(const mint& p){ x = (int)(1LL * x * p.x % mod); return *this; } mint& operator/=(const mint& p){ *this *= p.inverse(); return *this; } mint operator-() const { return mint(-x); } mint operator+(const mint& p) const { return mint(*this) += p; } mint operator-(const mint& p) const { return mint(*this) -= p; } mint operator*(const mint& p) const { return mint(*this) *= p; } mint operator/(const mint& p) const { return mint(*this) /= p; } bool operator==(const mint& p) const { return x == p.x; } bool operator!=(const mint& p) const { return x != p.x; } mint pow(int64_t n) const { mint res = 1, mul = x; while(n > 0){ if(n & 1) res *= mul; mul *= mul; n >>= 1; } return res; } mint inverse() const { return pow(mod - 2); } friend ostream& operator<<(ostream& os, const mint& p){ return os << p.x; } friend istream& operator>>(istream& is, mint& p){ int64_t val; is >> val; p = mint(val); return is; } }; int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); int N; cin >> N; vector A(N); for(int i = 0; i < N; ++i) cin >> A[i]; // 各 [L, R) の寄与度の更新式は、位置を i とすると ([i,i]は後で足す) // (i-L+1)*(R-i) -1 = -i^2 + (L+R-1)*i + (-LR+R-1) vector coeff_2(N + 1), coeff_1(N + 1), coeff_0(N + 1); constexpr int bound = 1e+9; ll prod = A[0]; int l = 0, r = 1; while(r < N){ if(prod * A[r] >= bound){ coeff_2[l] += -1, coeff_2[r] -= -1; coeff_1[l] += l + r - 1, coeff_1[r] -= l + r - 1; coeff_0[l] += ll(-l) * r + r - 1, coeff_0[r] -= ll(-l) * r + r - 1; while(l < r && prod * A[r] >= bound){ prod /= A[l++]; } } prod *= A[r++]; } coeff_2[l] += -1, coeff_2[r] -= -1; coeff_1[l] += l + r - 1, coeff_1[r] -= l + r - 1; coeff_0[l] += ll(-l) * r + r - 1, coeff_0[r] -= ll(-l) * r + r - 1; for(int i = 0; i < N; ++i){ coeff_0[i + 1] += coeff_0[i]; coeff_1[i + 1] += coeff_1[i]; coeff_2[i + 1] += coeff_2[i]; } vector W(N); for(int i = 0; i < N; ++i){ W[i] = 1 + coeff_2[i] * i * i + coeff_1[i] * i + coeff_0[i]; } mint ans = 1; for(int i = 0; i < N; ++i){ ans *= mint(A[i]).pow(W[i]); } cout << ans << '\n'; return 0; }