16400번: 소수 화폐 ↗

#include <bits/stdc++.h>

#define for1(s,n) for(int i = s; i < n; i++)
#define for1j(s,n) for(int j = s; j < n; j++)
#define foreach(k) for(auto i : k)
#define foreachj(k) for(auto j : k)
#define pb(a) push_back(a)
#define sz(a) a.size()
#define MOD 123456789ll

using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef vector <int> iv1;
typedef vector <vector<int>> iv2;
typedef vector <ll> llv1;
typedef unsigned int uint;
typedef vector <ull> ullv1;
typedef vector <vector <ull>> ullv2;

ll CC(llv1& coin, ll money, ll MX) {
    ll D[MX];
    fill(D, D+MX, 0);
    D[0] = 1;
    for(int i = coin.size()-1; i >=0; i--) {
        for(int j = coin[i]; j <= money; j++) {
            D[j] += D[j - coin[i]];
            D[j] %= MOD;
        }
    }
    return D[money] % MOD;
}

ll N;
ll prime[44000];

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    
    cin >> N;
    llv1 V;
    V.pb(2);
    for(int i = 3; i <= 40000; i +=2) {
        if(prime[i] == 0) {
            V.pb(i);
            for(int j = i + i; j <= 40000; j += i) {
                prime[j] = 1;
            }
        }
    }
    cout << CC(V, N, 44000);
    
    
}