結果
| 問題 |
No.3310 mod998
|
| コンテスト | |
| ユーザー |
 dyktr_06
|
| 提出日時 | 2025-10-24 22:45:00 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 98 ms / 2,000 ms |
| コード長 | 9,955 bytes |
| コンパイル時間 | 2,122 ms |
| コンパイル使用メモリ | 203,368 KB |
| 実行使用メモリ | 7,720 KB |
| 最終ジャッジ日時 | 2025-10-24 22:45:16 |
| 合計ジャッジ時間 | 6,814 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 33 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(int i = 0; i < (int)(n); ++i)
#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)
#define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define Sort(a) (sort((a).begin(), (a).end()))
#define RSort(a) (sort((a).rbegin(), (a).rend()))
#define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end()))
using i64 = int64_t;
using i128 = __int128_t;
using ll = long long;
using ul = unsigned long long;
using ull = unsigned long long;
using ld = long double;
using vi = vector<int>;
using vll = vector<long long>;
using vull = vector<unsigned long long>;
using vc = vector<char>;
using vst = vector<string>;
using vd = vector<double>;
using vld = vector<long double>;
using P = pair<long long, long long>;
template<class T> long long sum(const T &a){ return accumulate(a.begin(), a.end(), 0LL); }
template<class T> auto min(const T &a){ return *min_element(a.begin(), a.end()); }
template<class T> auto max(const T &a){ return *max_element(a.begin(), a.end()); }
const long long MINF = 0x7fffffffffff;
const long long INF = 0x1fffffffffffffff;
const long long MOD = 998244353;
const long double EPS = 1e-9;
const long double PI = acos(-1);
template<class T> inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; }
template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; }
template<class T, class U>
void inGraph(vector<vector<T>> &G, U n, U m, bool directed = true, bool zero_index = true){
G.resize(n);
for(int i = 0; i < m; i++){
int a, b;
cin >> a >> b;
if(!zero_index) a--, b--;
G[a].push_back(b);
if(!directed) G[b].push_back(a);
}
}
template <typename T>
long long binary_search(long long ok, long long ng, T check){
while(abs(ok - ng) > 1){
long long mid = (ok + ng) / 2;
if(check(mid)) ok = mid;
else ng = mid;
}
return ok;
}
template <typename T>
long double binary_search_real(long double ok, long double ng, T check, int iter = 100){
for(int i = 0; i < iter; ++i){
long double mid = (ok + ng) / 2;
if(check(mid)) ok = mid;
else ng = mid;
}
return ok;
}
long long trisum(long long a, long long b){
if(a > b) return 0;
long long res = ((b - a + 1) * (a + b)) / 2;
return res;
}
template <typename T>
T intpow(T x, int n){
T ret = 1;
while(n > 0) {
if(n & 1) (ret *= x);
(x *= x);
n >>= 1;
}
return ret;
}
template <typename T>
T getDivision(T a, T b){
if(b == 0) return -1;
if(a >= 0 && b > 0){
return a / b;
} else if(a < 0 && b > 0){
return a / b - (a % b != 0);
} else if(a >= 0 && b < 0){
return a / b;
} else{
return a / b + (a % b != 0);
}
}
template <typename T>
T getReminder(T a, T b){
if(b == 0) return -1;
if(a >= 0 && b > 0){
return a % b;
} else if(a < 0 && b > 0){
return ((a % b) + b) % b;
} else if(a >= 0 && b < 0){
return a % b;
} else{
return (abs(b) - abs(a % b)) % b;
}
}
template<class T, class U> inline T vin(T &vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; }
template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; }
template<class... T> void in(T&... a){ (cin >> ... >> a); }
void out(){ cout << '\n'; }
template<class T, class... Ts> void out(const T &a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
void fout(){ cout << endl; }
template<class T, class... Ts> void fout(const T &a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << endl; }
void debug(){ cerr << '\n'; }
template<class T, class... Ts> void debug(const T &a, const Ts&... b){ cerr << a; (cerr << ... << (cerr << ' ', b)); cerr << '\n'; }
namespace modcalc{
using i64 = long long;
i64 modpow(i64 x, i64 n, const i64 &m){
i64 ret = 1 % m;
x %= m;
while(n > 0){
if(n & 1) (ret *= x) %= m;
(x *= x) %= m;
n >>= 1;
}
return ret;
}
i64 modinv(i64 a, const i64 m){
i64 b = m, u = 1, v = 0;
while(b){
i64 t = a / b;
a -= t * b; std::swap(a, b);
u -= t * v; std::swap(u, v);
}
u %= m;
if(u < 0) u += m;
return u;
}
i64 modarithmeticsum(i64 a, i64 d, i64 n, const i64 m){
i64 m2 = m * 2;
a %= m2, n %= m2, d %= m2;
i64 b = (n + m2 - 1) * d % m2;
return ((n * (a * 2 + b) % m2) / 2) % m;
}
i64 modgeometricsum(i64 a, i64 r, i64 n, const i64 m){
a %= m;
if(r == 1){
n %= m;
return a * n % m;
}
return a * (modpow(r, n, m) + m - 1) % m * modinv(r - 1, m) % m;
}
i64 modgeometricsum2(i64 a, i64 r, i64 n, const i64 m){
a %= m;
if(r == 1){
n %= m;
return a * n % m;
}
i64 ret = 0;
i64 x = 1 % m;
i64 sum = 0;
for(int i = 0; n > 0; ++i){
if(n & 1){
(ret += x * modpow(r, sum, m) % m) %= m;
sum |= 1LL << i;
}
(x += x * modpow(r, 1LL << i, m) % m) %= m;
n >>= 1;
}
return a * ret % m;
}
// https://37zigen.com/tonelli-shanks-algorithm/
i64 modsqrt(i64 a, const i64 p){
a %= p;
if(a <= 1) return a;
// オイラーの規準
if(modpow(a, (p - 1) / 2, p) != 1) return -1;
i64 b = 1;
while(modpow(b, (p - 1) / 2, p) == 1) b++;
// p - 1 = m 2^e
i64 m = p - 1, e = 0;
while(m % 2 == 0) m >>= 1, e++;
// x = a^((m + 1) / 2) (mod p)
i64 x = modpow(a, (m - 1) / 2, p);
// y = a^{-1} x^2 (mod p)
i64 y = a * x % p * x % p;
(x *= a) %= p;
i64 z = modpow(b, m, p);
while(y != 1){
i64 j = 0, t = y;
while(t != 1){
(t *= t) %= p;
j++;
}
// e - j ビット目が 1
z = modpow(z, 1LL << (e - j - 1), p);
(x *= z) %= p;
(z *= z) %= p;
(y *= z) %= p;
e = j;
}
return x;
}
}
ll T;
void input(){
in(T);
}
void solve(){
ll n, m; in(n, m);
vst k(m); in(k);
const ll mod = 998;
vll cnt(mod, -1), cost(mod);
ll f = -1, looplen = -1, loopcost = -1, s = -1;
ll cur = 1;
cnt[1] = 0, cost[1] = 1;
rep(i, mod){
// out(i, cur);
ll nxt = cur * n % mod;
if(cnt[nxt] != -1){
f = cnt[nxt];
s = nxt;
looplen = cnt[cur] - cnt[nxt] + 1;
loopcost = (cost[cur] - cost[nxt] + nxt) % mod;
break;
}
cnt[nxt] = cnt[cur] + 1;
cost[nxt] = (cost[cur] + nxt) % mod;
cur = nxt;
}
rep(i, m){
if(k[i].size() < 10){
out(modcalc::modgeometricsum2(1LL, n, stoll(k[i]) + 1, 998));
}else{
// out(s, f, looplen, loopcost);
ll c = 0;
for(auto x : k[i]){
c *= 10;
c += (x - '0');
c %= mod * looplen;
}
c += 1;
c -= f; c %= mod * looplen;
if(c < 0) c += mod * looplen;
ll ans = cost[s] - s;
ans += (c / looplen) * loopcost;
ll r = c % looplen;
ll cur2 = s;
rep(j, r){
ans += cur2;
cur2 = (cur2 * n) % mod;
}
out(ans % mod);
}
}
}
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(20);
T = 1;
input();
while(T--) solve();
}