#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <vector>
using namespace std;
using ll = long long;
using db = long double; // or double, if TL is tight
using str = string; // yay python!
// pairs
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
#define mp make_pair
#define f first
#define s second
#define tcT template <class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT > using V = vector<T>;
tcT, size_t SZ > using AR = array<T, SZ>;
using vi = V<int>;
using vb = V<bool>;
using vl = V<ll>;
using vd = V<db>;
using vs = V<str>;
using vpi = V<pi>;
using vpl = V<pl>;
using vpd = V<pd>;
// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()
#define lb lower_bound
#define ub upper_bound
tcT > int lwb(V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); }
tcT > int upb(V<T> &a, const T &b) { return int(ub(all(a), b) - bg(a)); }
// loops
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i, a) ROF(i, 0, a)
#define rep(a) F0R(_, a)
#define each(a, x) for (auto &a : x)
const int MOD = (int)1e9 + 7; // 998244353;
const int MX = (int)2e5 + 5;
const ll BIG = 1e18; // not too close to LLONG_MAX
const db PI = acos((db)-1);
const int dx[4]{1, 0, -1, 0}, dy[4]{0, 1, 0, -1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(
int x) { // assert(x >= 0); // make C++11 compatible until USACO updates ...
return x == 0 ? 0 : 31 - __builtin_clz(x);
} // floor(log2(x))
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }
ll cdiv(ll a, ll b) {
return a / b + ((a ^ b) > 0 && a % b);
} // divide a by b rounded up
ll fdiv(ll a, ll b) {
return a / b - ((a ^ b) < 0 && a % b);
} // divide a by b rounded down
tcT > bool ckmin(T &a, const T &b) {
return b < a ? a = b, 1 : 0;
} // set a = min(a,b)
tcT > bool ckmax(T &a, const T &b) {
return a < b ? a = b, 1 : 0;
} // set a = max(a,b)
tcTU > T fstTrue(T lo, T hi, U f) {
++hi;
assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
T mid = lo + (hi - lo) / 2;
f(mid) ? hi = mid : lo = mid + 1;
}
return lo;
}
tcTU > T lstTrue(T lo, T hi, U f) {
--lo;
assert(lo <= hi); // assuming f is decreasing
while (lo < hi) { // find first index such that f is true
T mid = lo + (hi - lo + 1) / 2;
f(mid) ? lo = mid : hi = mid - 1;
}
return lo;
}
tcT > void remDup(vector<T> &v) { // sort and remove duplicates
sort(all(v));
v.erase(unique(all(v)), end(v));
}
tcTU > void erase(T &t, const U &u) { // don't erase
auto it = t.find(u);
assert(it != end(t));
t.erase(it);
} // element that doesn't exist from (multi)set
#define tcTUU tcT, class... U
inline namespace Helpers {
//////////// is_iterable
// https://stackoverflow.com/questions/13830158/check-if-a-variable-type-is-iterable
// this gets used only when we can call begin() and end() on that type
tcT, class = void > struct is_iterable : false_type {};
tcT > struct is_iterable<
T, void_t<decltype(begin(declval<T>())), decltype(end(declval<T>()))>>
: true_type {};
tcT > constexpr bool is_iterable_v = is_iterable<T>::value;
//////////// is_readable
tcT, class = void > struct is_readable : false_type {};
tcT > struct is_readable<T, typename std::enable_if_t<is_same_v<
decltype(cin >> declval<T &>()), istream &>>>
: true_type {};
tcT > constexpr bool is_readable_v = is_readable<T>::value;
//////////// is_printable
// // https://nafe.es/posts/2020-02-29-is-printable/
tcT, class = void > struct is_printable : false_type {};
tcT > struct is_printable<T, typename std::enable_if_t<is_same_v<
decltype(cout << declval<T>()), ostream &>>>
: true_type {};
tcT > constexpr bool is_printable_v = is_printable<T>::value;
} // namespace Helpers
inline namespace Input {
tcT > constexpr bool needs_input_v = !is_readable_v<T> && is_iterable_v<T>;
tcTUU > void re(T &t, U &...u);
tcTU > void re(pair<T, U> &p); // pairs
// re: read
tcT > typename enable_if<is_readable_v<T>, void>::type re(T &x) {
cin >> x;
} // default
tcT > void re(complex<T> &c) {
T a, b;
re(a, b);
c = {a, b};
} // complex
tcT > typename enable_if<needs_input_v<T>, void>::type
re(T &i); // ex. vectors, arrays
tcTU > void re(pair<T, U> &p) { re(p.f, p.s); }
tcT > typename enable_if<needs_input_v<T>, void>::type re(T &i) {
each(x, i) re(x);
}
tcTUU > void re(T &t, U &...u) {
re(t);
re(u...);
} // read multiple
// rv: resize and read vectors
void rv(size_t) {}
tcTUU > void rv(size_t N, V<T> &t, U &...u);
template <class... U> void rv(size_t, size_t N2, U &...u);
tcTUU > void rv(size_t N, V<T> &t, U &...u) {
t.rsz(N);
re(t);
rv(N, u...);
}
template <class... U> void rv(size_t, size_t N2, U &...u) { rv(N2, u...); }
// dumb shortcuts to read in ints
void decrement() {} // subtract one from each
tcTUU > void decrement(T &t, U &...u) {
--t;
decrement(u...);
}
#define ints(...) \
int __VA_ARGS__; \
re(__VA_ARGS__);
#define int1(...) \
ints(__VA_ARGS__); \
decrement(__VA_ARGS__);
} // namespace Input
inline namespace ToString {
tcT > constexpr bool needs_output_v = !is_printable_v<T> && is_iterable_v<T>;
// ts: string representation to print
tcT > typename enable_if<is_printable_v<T>, str>::type ts(T v) {
stringstream ss;
ss << fixed << setprecision(15) << v;
return ss.str();
} // default
tcT > str bit_vec(T t) { // bit vector to string
str res = "{";
F0R(i, sz(t)) res += ts(t[i]);
res += "}";
return res;
}
str ts(V<bool> v) { return bit_vec(v); }
template <size_t SZ> str ts(bitset<SZ> b) { return bit_vec(b); } // bit vector
tcTU > str ts(pair<T, U> p); // pairs
tcT >
typename enable_if<needs_output_v<T>, str>::type ts(T v); // vectors, arrays
tcTU > str ts(pair<T, U> p) { return "(" + ts(p.f) + ", " + ts(p.s) + ")"; }
tcT > typename enable_if<is_iterable_v<T>, str>::type ts_sep(T v, str sep) {
// convert container to string w/ separator sep
bool fst = 1;
str res = "";
for (const auto &x : v) {
if (!fst) res += sep;
fst = 0;
res += ts(x);
}
return res;
}
tcT > typename enable_if<needs_output_v<T>, str>::type ts(T v) {
return "{" + ts_sep(v, ", ") + "}";
}
// for nested DS
template <int, class T>
typename enable_if<!needs_output_v<T>, vs>::type ts_lev(const T &v) {
return {ts(v)};
}
template <int lev, class T>
typename enable_if<needs_output_v<T>, vs>::type ts_lev(const T &v) {
if (lev == 0 || !sz(v)) return {ts(v)};
vs res;
for (const auto &t : v) {
if (sz(res)) res.bk += ",";
vs tmp = ts_lev<lev - 1>(t);
res.ins(end(res), all(tmp));
}
F0R(i, sz(res)) {
str bef = " ";
if (i == 0) bef = "{";
res[i] = bef + res[i];
}
res.bk += "}";
return res;
}
} // namespace ToString
inline namespace Output {
template <class T> void pr_sep(ostream &os, str, const T &t) { os << ts(t); }
template <class T, class... U>
void pr_sep(ostream &os, str sep, const T &t, const U &...u) {
pr_sep(os, sep, t);
os << sep;
pr_sep(os, sep, u...);
}
// print w/ no spaces
template <class... T> void pr(const T &...t) { pr_sep(cout, "", t...); }
// print w/ spaces, end with newline
void ps() { cout << "\n"; }
template <class... T> void ps(const T &...t) {
pr_sep(cout, " ", t...);
ps();
}
// debug to cerr
template <class... T> void dbg_out(const T &...t) {
pr_sep(cerr, " | ", t...);
cerr << endl;
}
void loc_info(int line, str names) {
cerr << "Line(" << line << ") -> [" << names << "]: ";
}
template <int lev, class T> void dbgl_out(const T &t) {
cerr << "\n\n" << ts_sep(ts_lev<lev>(t), "\n") << "\n" << endl;
}
#ifdef LOCAL
#define dbg(...) loc_info(__LINE__, #__VA_ARGS__), dbg_out(__VA_ARGS__)
#define dbgl(lev, x) loc_info(__LINE__, #x), dbgl_out<lev>(x)
#else // don't actually submit with this
#define dbg(...) 0
#define dbgl(lev, x) 0
#endif
const clock_t beg = clock();
#define dbg_time() dbg((db)(clock() - beg) / CLOCKS_PER_SEC)
} // namespace Output
inline namespace FileIO {
void setIn(str s) { freopen(s.c_str(), "r", stdin); }
void setOut(str s) { freopen(s.c_str(), "w", stdout); }
void setIO(str s = "") {
cin.tie(0)->sync_with_stdio(0); // unsync C / C++ I/O streams
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) setIn(s + ".in"), setOut(s + ".out"); // for old USACO
}
} // namespace FileIO
// conditions:
// <M unused out of negatives or <M unused out of positives
// you can split at some positive index such that <M unused on both sides
int M;
void add_min(vi &dp, int sum, int num) {
assert(num > 0);
if (sum > 0) {
R0F(i, sz(dp) - sum) {
if (dp[i] != M) ckmin(dp[i + sum], dp[i] + num);
}
} else {
FOR(i, -sum, sz(dp)) {
if (dp[i] != M) ckmin(dp[i + sum], dp[i] + num);
}
}
}
void add_max(vi &dp, int sum, int num) {
if (sum > 0) {
// dbg("ADD MAX", sum, num);
R0F(i, sz(dp) - sum) {
if (dp[i] != -1) ckmax(dp[i + sum], dp[i] + num);
}
// dbg("DONE MAX", sum, num);
} else {
FOR(i, -sum, sz(dp)) {
if (dp[i] != -1) ckmax(dp[i + sum], dp[i] + num);
}
}
}
ll ans = -1;
void add_min_all(vi &v, int x, ll num) {
ckmin(num, (ll)M - 1);
// dbg("add min all", x, num);
for (int j = 1;; j *= 2) {
ckmin(j, (int)num);
if (j == 0) break;
num -= j;
add_min(v, j * x, j);
}
}
void add_max_all(vi &v, int x, ll num) {
ckmin(num, (ll)M - 1);
for (int j = 1;; j *= 2) {
ckmin(j, (int)num);
if (j == 0) break;
num -= j;
add_max(v, j * x, j);
}
}
void solve(vl A, ll L) {
ll tot_sum = 0;
FOR(i, -M, M + 1) tot_sum += i * A.at(i + M);
if (tot_sum + M * M < L) return;
V<vi> psums(M + 1, vi(2 * M * M + 1, M));
psums.ft.at(M * M) = 0;
FOR(x, -M, 0) { add_min_all(psums.at(0), x, A.at(x + M)); }
FOR(x, 1, M + 1) {
psums.at(x) = psums.at(x - 1);
add_min_all(psums.at(x), x, A.at(x + M));
}
V<vi> suf_sums(M + 2, vi(M * M, -1));
suf_sums.bk.at(0) = 0;
ROF(x, 1, M + 1) {
suf_sums.at(x) = suf_sums.at(x + 1);
add_max_all(suf_sums.at(x), x, A.at(x + M));
}
ll sum_so_far = 0, num_so_far = 0;
FOR(i, -M, 1) {
sum_so_far += A.at(i + M) * i;
num_so_far += A.at(i + M);
}
FOR(x, 1, M + 1) {
// sum_so_far - i + ? * x + j = L
FOR(i, -M * M, M * x) if (psums.at(x - 1).at(i + M * M) < M) {
ll rem = L - sum_so_far + i; // 5 - ()
if (rem < 0) continue;
int hi_j = (M * M - 1 - rem % x) / x * x + (rem % x);
for (int j = hi_j; j >= 0; j -= x) {
ll need_x = (rem - j) / x;
if (need_x > A.at(x + M)) break;
if (suf_sums.at(x + 1).at(j) != -1) {
ckmax(ans, num_so_far - psums.at(x - 1).at(i + M * M) +
suf_sums.at(x + 1).at(j) + need_x);
}
}
}
sum_so_far += A.at(x + M) * x;
num_so_far += A.at(x + M);
}
}
int main() {
// read read read
setIO();
re(M);
ll L;
re(L);
vl A(2 * M + 1);
re(A);
solve(A, L);
reverse(all(A));
solve(A, -L);
if (ans == -1) ps("impossible");
else ps(ans);
// everything < M*M:
// you should actually read the stuff at the bottom
}
/* stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
* DON'T GET STUCK ON ONE APPROACH
*/
Compilation message
vault.cpp: In function 'void FileIO::setIn(str)':
vault.cpp:312:28: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
312 | void setIn(str s) { freopen(s.c_str(), "r", stdin); }
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~
vault.cpp: In function 'void FileIO::setOut(str)':
vault.cpp:313:29: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
313 | void setOut(str s) { freopen(s.c_str(), "w", stdout); }
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Correct |
2 ms |
600 KB |
Output is correct |
| 3 |
Correct |
2 ms |
648 KB |
Output is correct |
| 4 |
Correct |
2 ms |
576 KB |
Output is correct |
| 5 |
Correct |
2 ms |
596 KB |
Output is correct |
| 6 |
Correct |
1 ms |
596 KB |
Output is correct |
| 7 |
Correct |
1 ms |
596 KB |
Output is correct |
| 8 |
Correct |
1 ms |
596 KB |
Output is correct |
| 9 |
Incorrect |
3 ms |
596 KB |
Output isn't correct |
| 10 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Correct |
2 ms |
600 KB |
Output is correct |
| 3 |
Correct |
2 ms |
648 KB |
Output is correct |
| 4 |
Correct |
2 ms |
576 KB |
Output is correct |
| 5 |
Correct |
2 ms |
596 KB |
Output is correct |
| 6 |
Correct |
1 ms |
596 KB |
Output is correct |
| 7 |
Correct |
1 ms |
596 KB |
Output is correct |
| 8 |
Correct |
1 ms |
596 KB |
Output is correct |
| 9 |
Incorrect |
3 ms |
596 KB |
Output isn't correct |
| 10 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Correct |
2 ms |
600 KB |
Output is correct |
| 3 |
Correct |
2 ms |
648 KB |
Output is correct |
| 4 |
Correct |
2 ms |
576 KB |
Output is correct |
| 5 |
Correct |
2 ms |
596 KB |
Output is correct |
| 6 |
Correct |
1 ms |
596 KB |
Output is correct |
| 7 |
Correct |
1 ms |
596 KB |
Output is correct |
| 8 |
Correct |
1 ms |
596 KB |
Output is correct |
| 9 |
Incorrect |
3 ms |
596 KB |
Output isn't correct |
| 10 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Correct |
2 ms |
600 KB |
Output is correct |
| 3 |
Correct |
2 ms |
648 KB |
Output is correct |
| 4 |
Correct |
2 ms |
576 KB |
Output is correct |
| 5 |
Correct |
2 ms |
596 KB |
Output is correct |
| 6 |
Correct |
1 ms |
596 KB |
Output is correct |
| 7 |
Correct |
1 ms |
596 KB |
Output is correct |
| 8 |
Correct |
1 ms |
596 KB |
Output is correct |
| 9 |
Incorrect |
3 ms |
596 KB |
Output isn't correct |
| 10 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Correct |
2 ms |
600 KB |
Output is correct |
| 3 |
Correct |
2 ms |
648 KB |
Output is correct |
| 4 |
Correct |
2 ms |
576 KB |
Output is correct |
| 5 |
Correct |
2 ms |
596 KB |
Output is correct |
| 6 |
Correct |
1 ms |
596 KB |
Output is correct |
| 7 |
Correct |
1 ms |
596 KB |
Output is correct |
| 8 |
Correct |
1 ms |
596 KB |
Output is correct |
| 9 |
Incorrect |
3 ms |
596 KB |
Output isn't correct |
| 10 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
212 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
