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- /*
- ∧_∧
- ( ・ω・。)つ━☆・*。
- ⊂ ノ ・゜
- しーJ Accepted
- */
- // #pragma GCC optimize("O3")
- // #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
- #include <bits/stdc++.h>
- #include <ext/pb_ds/assoc_container.hpp>
- #include <ext/pb_ds/tree_policy.hpp>
- #define ll long long
- #define all(x) begin(x), end(x)
- #define x first
- #define y second
- #define int long long
- using namespace std;
- using namespace __gnu_pbds;
- typedef long double ld;
- template<typename T>
- using kawaii_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
- const ld PI = atan2(0, -1);
- void seriy() {
- ios::sync_with_stdio(0);
- cin.tie(0);
- cout.tie(0);
- cout << fixed << setprecision(14);
- #ifdef _offline
- freopen("input.txt", "r", stdin);
- freopen("output.txt", "w", stdout);
- #endif
- }
- const int MAXN = 1e5 + 10;
- const int MAXM = 600;
- const int INF = 1e18 + 7;
- const int BASE = 47;
- const int MOD = 998244353;
- const int MAXLOG = 61;
- const ld EPS = 1e-8;
- ld binpow(ld a, int pw) {
- if(pw == 0) return 1;
- if(pw % 2) {
- return binpow(a, pw - 1) * a;
- }
- else {
- a *= a;
- return binpow(a, pw / 2);
- }
- }
- signed main() {
- seriy();
- int n;
- ld m, t;
- cin >> n >> m >> t;
- vector<pair<ld, ld>> a(n);
- for(int i = 0; i < n; i++) {
- cin >> a[i].x >> a[i].y;
- a[i].y = (a[i].y / 1e6) + 1;
- }
- sort(all(a), [&](pair<ld, ld> a, pair<ld, ld> b) {
- return a.y < b.y;
- });
- // for(auto i : a) {
- // cerr << i.x << " " << i.y << '\n';
- // }
- vector<ld> pw(n);
- for(int i = 0; i < n; i++) {
- pw[i] = binpow(a[i].y, m);
- }
- int cnt = 100;
- ld l = 0, r = INF;
- while(cnt--) {
- ld mid = (l + r) / 2.;
- ld need = mid;
- ld sum = 0;
- vector<ld> cnt(n), now(n), start(n);
- for(int i = 0; i < n; i++) {
- ld can = min(need, a[i].x);
- cnt[i] = can;
- start[i] = can;
- need -= can;
- }
- int cur = n - 1;
- for(int i = 0; i < m; i++) {
- ld tt = t;
- while(tt > 0) {
- // cerr << tt << '\n';
- if(abs(cnt[cur] - now[cur]) < EPS) {
- cur--;
- }
- if(cur < 0) break;
- // cerr << a[cur].y << '\n';
- cnt[cur] = start[cur] * binpow(a[cur].y, i);
- // cerr << cur << '\n';
- // cerr << abs(cnt[cur] - now[cur]) << " " << tt << '\n';
- ld out = min(abs(cnt[cur] - now[cur]), tt);
- now[cur] += out;
- tt -= out;
- }
- if(cur < 0) break;
- }
- if(abs(cnt[0] - now[0]) < EPS) {
- l = mid;
- }
- else {
- r = mid;
- }
- }
- cout << r;
- return 0;
- }
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