#ifdef LOCAL #define _GLIBCXX_DEBUG #define __clock__ #else #pragma GCC optimize("Ofast") #endif #include using namespace std; using ll = long long; using ld = long double; using VI = vector; using VV = vector; using VS = vector; using PII = pair; // tourist set template string to_string(pair p); template string to_string(tuple p); template string to_string(tuple p); string to_string(const string& s) { return '"' + s + '"'; } string to_string(const char* s) { return to_string((string) s); } string to_string(bool b) { return (b ? "true" : "false"); } string to_string(vector v) { bool first = true; string res = "{"; for (int i = 0; i < static_cast(v.size()); i++) { if (!first) { res += ", "; } first = false; res += to_string(v[i]); } res += "}"; return res; } template string to_string(bitset v) { string res = ""; for (size_t i = 0; i < N; i++) { res += static_cast('0' + v[i]); } return res; } template string to_string(A v) { bool first = true; string res = "{"; for (const auto &x : v) { if (!first) { res += ", "; } first = false; res += to_string(x); } res += "}"; return res; } template string to_string(pair p) { return "(" + to_string(p.first) + ", " + to_string(p.second) + ")"; } template string to_string(tuple p) { return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")"; } template string to_string(tuple p) { return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")"; } void debug_out() { cerr << '\n'; } template void debug_out(Head H, Tail... T) { cerr << " " << to_string(H); debug_out(T...); } #ifdef LOCAL #define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #else #define debug(...) 42 #endif // tourist set end templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b()) #define MP make_pair #define p_yes() p("Yes") #define p_no() p("No") ll SUM(VI& V){ return accumulate(ALL(V), 0LL); } ll MIN(VI& V){return *min_element(ALL(V));} ll MAX(VI& V){return *max_element(ALL(V));} void print_vector(VI& V){ ll n = V.size(); rep(i, n){ if(i) cout << ' '; cout << V[i]; } cout << endl; } ll gcd(ll a,ll b){ if(b == 0) return a; return gcd(b,a%b); } ll lcm(ll a,ll b){ ll g = gcd(a,b); return a / g * b; } // long double using ld = long double; #define EPS (1e-14) #define equals(a,b) (fabs((a)-(b)) < EPS) void no(){p_no(); exit(0);} void yes(){p_yes(); exit(0);} const ll mod = 1e9 + 7; const ll inf = 1e18; const double PI = acos(-1); // Matrix (long double ver) using Mat = vector>; // Matrix Library Mat mat_mul(const Mat& x, const Mat& y){ int a = x.size(); int b = x[0].size(); int c = y[0].size(); Mat z(a, vector(c, 0)); FOR(i, 0, a){ FOR(j, 0, c){ FOR(k, 0, b){ z[i][j] += x[i][k] * y[k][j]; //z[i][j] %= mod; // 必要であれば } } } return z; } Mat mat_pow(const Mat& x, ll k){ int n = x.size(); Mat y(n, vector(n, 0)); FOR(i, 0, n){ y[i][i] = 1; } auto z = x; if(k==0) return y; if(k==1) return z; if(k%2==0){ return mat_pow(mat_mul(x, x), k/2); }else{ return mat_mul(x, mat_pow(x, k-1)); } } void print_mat(Mat x){ ll H = x.size(); FOR(i, 0, H){ for(ld v : x[i]){ cout << v << ' '; } cout << endl; } } int main(){ cin.tie(0); ios::sync_with_stdio(false); // input ll N,M,K; cin>>N>>M>>K; ld p,q;cin>>p>>q; VI B(N); rep(i, N) cin >> B[i]; ld warp = p/q; ld stay = 1-warp; Mat A = { {stay, warp}, {warp, stay} }; print_mat(A); Mat P = mat_pow(A, K); // (1, 0) : 存在から開始 Mat I = { {1}, {0} }; // (0, 1) : コップ外から開始 Mat J = { {0}, {1} }; ld exist_to_exist = mat_mul(P, I)[0][0]; ld out_to_exist = mat_mul(P, J)[0][0]; ld sum = 0; rep(i,M){ sum += B[i] * exist_to_exist; } FOR(i, M, N){ sum += B[i] * out_to_exist; } cout << setprecision(20); p(sum); return 0; }