cses money sums solution
#include <bits/stdc++.h>
using namespace std;
int main() {
int n;
cin >> n;
int max_sum = n*1000;
vector<int> x(n);
for (int&v : x) cin >> v;
vector<vector<bool>> dp(n+1,vector<bool>(max_sum+1,false));
dp[0][0] = true;
for (int i = 1; i <= n; i++) {
for (int j = 0; j <= max_sum; j++) {
dp[i][j] = dp[i-1][j];
int left = j-x[i-1];
if (left >= 0 && dp[i-1][left]) {
dp[i][j] = true;
}
}
}
vector<int> possible;
for (int j = 1; j <= max_sum; j++) {
if (dp[n][j]) {
possible.push_back(j);
}
}
cout << possible.size() << endl;
for (int v : possible) {
cout << v << ' ';
}
cout << endl;
}