#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using ll = long long;
using ld = long double;
using ull = unsigned long long;
#define endl "\n"
typedef pair<int, int> Pii;
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define REP3(i, m, n) for (int i = (m); (i) < int(n); ++ (i))
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(x) begin(x), end(x)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define fore(i,a) for(auto &i:a)
#define all(s) (s).begin(),(s).end()
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define FOR_(n) for (ll _ = 0; (_) < (ll)(n); ++(_))
#define FOR(i, n) for (ll i = 0; (i) < (ll)(n); ++(i))
#define se second
#define pb push_back
#define P pair<ll,ll>
#define PQminll priority_queue<ll, vector<ll>, greater<ll>>
#define PQmaxll priority_queue<ll,vector<ll>,less<ll>>
#define PQminP priority_queue<P, vector<P>, greater<P>>
#define PQmaxP priority_queue<P,vector<P>,less<P>>
#define NP next_permutation
#define die(a) {cout<<a<<endl;return 0;}
#define dier(a) {return a;}
//const ll mod = 1000000009;
const ll mod = 998244353;
//const ll mod = 1000000007;
const ll inf = 4000000000000000000ll;
const ld eps = ld(0.00000000001);
static const long double pi = 3.141592653589793;
template<class T>void vcin(vector<T> &n){for(int i=0;i<int(n.size());i++) cin>>n[i];}
template<class T,class K>void vcin(vector<T> &n,vector<K> &m){for(int i=0;i<int(n.size());i++) cin>>n[i]>>m[i];}
template<class T>void vcout(vector<T> &n){for(int i=0;i<int(n.size());i++){cout<<n[i]<<" ";}cout<<endl;}
template<class T>void vcin(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cin>>n[i][j];}}}
template<class T>void vcout(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cout<<n[i][j]<<" ";}cout<<endl;}cout<<endl;}
void yes(bool a){cout<<(a?"yes":"no")<<endl;}
void YES(bool a){cout<<(a?"YES":"NO")<<endl;}
void Yes(bool a){cout<<(a?"Yes":"No")<<endl;}
void possible(bool a){ cout<<(a?"possible":"impossible")<<endl; }
void Possible(bool a){ cout<<(a?"Possible":"Impossible")<<endl; }
void POSSIBLE(bool a){ cout<<(a?"POSSIBLE":"IMPOSSIBLE")<<endl; }
#define FOR_R(i, n) for (ll i = (ll)(n)-1; (i) >= 0; --(i))
template<class T>auto min(const T& a){ return *min_element(all(a)); }
//template<class T>auto max(const T& a){ return *max_element(all(a)); }
template<class T,class F>void print(pair<T,F> a){cout<<a.fi<<" "<<a.se<<endl;}
template<class T>bool chmax(T &a,const T b) { if (a<b) { a=b; return 1; } return 0;}
template<class T>bool chmin(T &a,const T b) { if (b<a) { a=b; return 1; } return 0;}
template<class T> void ifmin(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<class T> void ifmax(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
ll fastgcd(ll u,ll v){ll shl=0;while(u&&v&&u!=v){bool eu=!(u&1);bool ev=!(v&1);if(eu&&ev){++shl;u>>=1;v>>=1;}else if(eu&&!ev){u>>=1;}else if(!eu&&ev){v>>=1;}else if(u>=v){u=(u-v)>>1;}else{ll tmp=u;u=(v-u)>>1;v=tmp;}}return !u?v<<shl:u<<shl;}
ll modPow(ll a, ll n, ll mod) { if(mod==1) return 0;ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
vector<ll> divisor(ll x){ vector<ll> ans; for(ll i = 1; i * i <= x; i++){ if(x % i == 0) {ans.push_back(i); if(i*i!=x){ ans.push_back(x / ans[i]);}}}sor(ans); return ans; }
ll pop(ll x){return __builtin_popcountll(x);}
ll poplong(ll x){ll y=-1;while(x){x/=2;y++;}return y;}
P hyou(P a){ll x=fastgcd(abs(a.fi),abs(a.se));a.fi/=x;a.se/=x;if(a.se<0){a.fi*=-1;a.se*=-1;}return a;}
P Pplus(P a,P b){ return hyou({a.fi*b.se+b.fi*a.se,a.se*b.se});}
P Ptimes(P a,ll b){ return hyou({a.fi*b,a.se});}
P Ptimes(P a,P b){ return hyou({a.fi*b.fi,a.se*b.se});}
P Pminus(P a,P b){ return hyou({a.fi*b.se-b.fi*a.se,a.se*b.se});}
P Pgyaku(P a){ return hyou({a.se,a.fi});}
void cincout(){
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
cout<< fixed << setprecision(15);
}
vector<ll> solve(vector<ll> a,ll p,ll x,ll q){
if(x==0) return a;
//a[i] = max_{0<=j<=x} a[i+p*j] + q*j
if(p==-1){
rever(a);
auto b=solve(a,1,x,q);
rever(b);
return b;
}
ll n=a.size();
//a[i] = -q*i + max_{0<=j<=x} a[i+j] + q*(i+j)
for(int i=0;i<n;i++) a[i]+=q*i;
vector<ll> b(n);
deque<ll> id;
ll l=0;
for(int i=0;i<n;i++){
while(l<n&&l<=i+x){
while(id.size()&&a[id.back()]<a[l]) id.pop_back();
id.push_back(l);
l++;
}
while(id.size()&&id.front()<i) id.pop_front();
b[i]=a[id.front()];
}
for(int i=0;i<n;i++) b[i]-=q*i;
return b;
}
int main(){
cincout();
//小さい方から追加していく
//全部追加しても L に到達しなかったら？
//全部 -1 倍すれば到達したことになる
//負を全部入れても駄目なら絶対駄目
ll m,l;
cin>>m>>l;
vector<ll> a(2*m+1);
vcin(a);
ll sum=0;
for(int i=0;i<=2*m;i++) sum+=a[i]*(i-m);
if(sum<l){
l*=-1;
rever(a);
}
ll sum2=0;
for(int i=0;i<=m;i++) sum2+=a[i]*(i-m);
if(sum2>l){
cout<<"Impossible"<<endl;
}
vector<ll> used(2*m+1);
for(int i=0;i<=m;i++) used[i]=a[i];
for(int i=1;i<=m;i++){
if(sum2+a[i+m]*i<=l){
sum2+=a[i+m]*i;
used[i+m]=a[i+m];
}
else{
ll v=(l-sum2)/i;
used[i+m]=v;
sum2+=v*i;
}
}
ll cnt=0;
for(auto e:used) cnt+=e;
vector<ll> dp(4*m*m+1,-inf);
ll md=2*m*m;
//dp[md] が l
dp[md-l+sum2]=cnt;
for(int i=0;i<=2*m;i++){
{
ll w=i+m;
ll x=used[i];
//x 個を削除する遷移
//dp[i] = max_{0<=j<=x} dp[i+w*j]-j
for(int j=0;j<abs(w);j++){
vector<ll> dp2;
for(int k=j;k<=4*m*m;k+=abs(w)) dp2.pb(dp[k]);
//dp2[i] = max_{0<=j<=x} dp2[i+abs(w)/w*j]-j
dp2=solve(dp2,abs(w)/w,x,-1);
for(int k=j;k<=4*m*m;k+=abs(w)) dp[k]=dp2[(k-j)/abs(w)];
}
}
{
ll w=i+m;
ll x=a[i]-used[i];
//x 個を追加する遷移
//dp[i] = max_{0<=j<=x} dp[i-w*j]+j
for(int j=0;j<abs(w);j++){
vector<ll> dp2;
for(int k=j;k<=4*m*m;k+=abs(w)) dp2.pb(dp[k]);
//dp2[i] = max_{0<=j<=x} dp2[i-abs(w)/w*j]+j
dp2=solve(dp2,-abs(w)/w,x,1);
for(int k=j;k<=4*m*m;k+=abs(w)) dp[k]=dp2[(k-j)/abs(w)];
}
}
}
if(dp[md]<-inf/2){
cout<<"Impossible"<<endl;
}
else{
cout<<dp[md]<<endl;
}
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
344 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 |
Incorrect |
1 ms |
344 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
348 KB |
Output is correct |
| 2 |
Correct |
4 ms |
348 KB |
Output is correct |
| 3 |
Incorrect |
3 ms |
348 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
348 KB |
Output is correct |
| 2 |
Correct |
4 ms |
348 KB |
Output is correct |
| 3 |
Incorrect |
3 ms |
348 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
348 KB |
Output is correct |
| 2 |
Correct |
4 ms |
348 KB |
Output is correct |
| 3 |
Incorrect |
3 ms |
348 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
344 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
348 KB |
Output is correct |
| 2 |
Correct |
4 ms |
348 KB |
Output is correct |
| 3 |
Incorrect |
3 ms |
348 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
344 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
348 KB |
Output is correct |
| 2 |
Correct |
4 ms |
348 KB |
Output is correct |
| 3 |
Incorrect |
3 ms |
348 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
344 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
344 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
