#include #define rep(i,a,b) for(int i=a;i=b;i--) #define fore(i,a) for(auto &i:a) #define all(x) (x).begin(),(x).end() //#pragma GCC optimize ("-O3") using namespace std; void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); } typedef long long ll; const int inf = INT_MAX / 2; const ll infl = 1LL << 60; templatebool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; } templatebool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; } //--------------------------------------------------------------------------------------------------- template using min_priority_queue = priority_queue, greater>; ll mul(ll a, ll b) { if(a==0) return 0; if(infl/a> N >> A >> B >> C; rep(mo, 0, N) rep(isUpper, 0, 2) { dp[mo][isUpper] = infl; vis[mo][isUpper] = 0; } P[1] = PM[1] = 1; rep(i, 2, N) { P[i] = mul(P[i - 1], i); PM[i] = (1LL * PM[i - 1] * i) % N; } min_priority_queue>> que; dp[1][0] = 0; que.push({0, {1, 0}}); while(!que.empty()) { auto q = que.top(); que.pop(); ll cst = q.first; int mo = q.second.first; int isUpper = q.second.second; if (vis[mo][isUpper]) continue; vis[mo][isUpper] = 1; if (mo == 0) { cout << cst << endl; return; } int mo2, isUpper2; // Op.1 mo2 = (mo + 1) % N; isUpper2 = isUpper; if (mo + 1 == N) isUpper2 = 1; if (chmin(dp[mo2][isUpper2], cst + A)) que.push({ dp[mo2][isUpper2], {mo2, isUpper2} }); // Op.2 mo2 = mo; isUpper2 = isUpper; ll b2 = B; rep(k, 2, 64) { if (isUpper2 == 0 && N <= mul(mo2, mo)) isUpper2 = 1; mo2 = (1LL * mo2 * mo) % N; b2 = mul(b2, B); if (chmin(dp[mo2][isUpper2], cst + b2)) que.push({ dp[mo2][isUpper2], {mo2, isUpper2} }); } // Op.3 mo2 = PM[mo]; if (isUpper == 0) { isUpper2 = isUpper; if (N <= P[mo]) isUpper2 = 1; if (chmin(dp[mo2][isUpper2], cst + C)) que.push({ dp[mo2][isUpper2], {mo2, isUpper2} }); } else { if (chmin(dp[0][1], cst + C)) que.push({ dp[0][1], {0, 1} }); } } } /* ## 前提知識 ## 解法 */