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Modulo Subsequences
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Modulo Subsequences
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#include<bits/stdc++.h>
using namespace std;
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int n,m;
cin>>n>>m;
vector<int>v(n);
for(int i=0;i<n;i++){
cin>>v[i];
}
if(n==1){
cout<<v[0]%m<<"\n";
return 0;
}
int mid=((n+1)/2);
vector<int>sums;
for(int conf=0;conf<(1<<mid);++conf){
int sum=0;
for(int i=0;i<mid;++i){
if((conf&(1<<i))!=0){
sum=(sum+v[i])%m;
}
}
sums.push_back(sum);
}
sort(sums.begin(),sums.end());
int ans =0;
for(int64_t conf=0;conf<(1LL<<n);conf+= 1LL<<mid){
int sum=0;
for(int i=mid;i<n;++i){
if((conf&(1LL<<i))!=0){
sum = (sum+v[i])%m;
}
}
int need = (m-1-sum+m)%m;
int pos = upper_bound(sums.begin(),sums.end(),need) - sums.begin() -1;
if(pos<0){
pos = (int)sums.size() -1;
}
ans=max(ans,(sum + sums[pos])%m);
}
cout<<ans<<"\n";
}