显然这题就是一个

恰好的$01$背包 + 路径输出 + $INT\_128$

但是竟然$WA$了 ,Σ(っ °Д °;)っ

#include <iostream>
#include <vector>
#include <map>
#include <cstring>
#include <queue>
#include <algorithm>
using namespace std;
#define ll long long
#define endl '\n'

inline __int128 read(){
    __int128 x=0,f=1;
    char ch=getchar();
    while(ch<'0'||ch>'9'){
        if(ch=='-')
            f=-1;
        ch=getchar();
    }
    while(ch>='0'&&ch<='9'){
        x=x*10+ch-'0';
        ch=getchar();
    }
    return x*f;
}

inline void print(__int128 x){
    if(x<0){
        putchar('-');
        x=-x;
    }
    if(x>9)
        print(x/10);
    putchar(x%10+'0');
}

typedef pair<int,int> pii;
map<pii,int> path;

const int N  = 1e4+5;

__int128 f[N];
int ans[N],idx;

void solve()
{
    int n;cin>>n;
    int sum = 0 ;

    f[0] = 1;

    for(int i=1;i<=n;i++)
    {
        for(int j = n;j>=i ;j -- )
        {
            if(f[j]<f[j-i]*i)
                path[{i,j}] = 1;
            f[j] = max(f[j],f[j-i]*i);
        }
    }

    int t = n ;
    for(int i = n;i>=1;i -- )
    {
        if(path[{i,t}]){
            ans[++idx] = i;
            t-=i;
        }
    }

    for(int i = idx;i>=1;i--)
        cout<<ans[i]<<" ";
        cout<<endl;

        print(f[n]);
}
int main()
{
    solve();
    return 0;
}