結果
| 問題 |
No.2993 冪乗乗 mod 冪乗
|
| コンテスト | |
| ユーザー |
 tko919
|
| 提出日時 | 2024-12-18 08:33:45 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 44,049 bytes |
| コンパイル時間 | 8,326 ms |
| コンパイル使用メモリ | 347,348 KB |
| 実行使用メモリ | 354,168 KB |
| 最終ジャッジ日時 | 2024-12-18 08:37:33 |
| 合計ジャッジ時間 | 227,467 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 11 WA * 1 TLE * 18 |
ソースコード
#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
template <typename T> inline bool chmax(T &a, T b) {
if (a < b) {
a = b;
return 1;
}
return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
if (a > b) {
a = b;
return 1;
}
return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
assert(y != 0);
if (y < 0)
x = -x, y = -y;
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
assert(y != 0);
if (y < 0)
x = -x, y = -y;
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << "P(" << p.first << ", " << p.second << ")";
return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
os << "{";
for (int i = 0; i < vec.size(); i++) {
os << vec[i] << (i + 1 == vec.size() ? "" : ", ");
}
os << "}";
return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
os << "{";
for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
os << "(" << itr->first << ", " << itr->second << ")";
itr++;
if (itr != map_var.end())
os << ", ";
itr--;
}
os << "}";
return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) {
os << "{";
for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
os << *itr;
++itr;
if (itr != set_var.end())
os << ", ";
itr--;
}
os << "}";
return os;
}
#ifdef LOCAL
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
cerr << '\n';
}
template <typename T1, typename T2, typename... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
for (; a[i] != ',' && a[i] != '\0'; i++)
cerr << a[i];
cerr << ":" << b << " ";
_show(i + 1, a, c...);
}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memmove(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ)
ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir)
load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir)
load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir)
load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T> void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T> void rd_integer(T &x) {
if (pil + 100 > pir)
load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') {
minus = 1, c = ibuf[pil++];
}
}
x = 0;
while ('0' <= c) {
x = x * 10 + (c & 15), c = ibuf[pil++];
}
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus)
x = -x;
}
}
void rd(int &x) {
rd_integer(x);
}
void rd(ll &x) {
rd_integer(x);
}
void rd(i128 &x) {
rd_integer(x);
}
void rd(uint &x) {
rd_integer(x);
}
void rd(ull &x) {
rd_integer(x);
}
void rd(u128 &x) {
rd_integer(x);
}
void rd(double &x) {
rd_real(x);
}
void rd(long double &x) {
rd_real(x);
}
template <class T, class U> void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T> void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T> void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T> void rd(array<T, N> &x) {
for (auto &d : x)
rd(d);
}
template <class T> void rd(vector<T> &x) {
for (auto &d : x)
rd(d);
}
void read() {}
template <class H, class... T> void read(H &h, T &...t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ)
flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c : s)
wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++)
wt(s[i]);
}
template <typename T> void wt_integer(T x) {
if (por > SZ - 100)
flush();
if (x < 0) {
obuf[por++] = '-', x = -x;
}
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T> void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) {
wt_integer(x);
}
void wt(ll x) {
wt_integer(x);
}
void wt(i128 x) {
wt_integer(x);
}
void wt(uint x) {
wt_integer(x);
}
void wt(ull x) {
wt_integer(x);
}
void wt(u128 x) {
wt_integer(x);
}
void wt(double x) {
wt_real(x);
}
void wt(long double x) {
wt_real(x);
}
template <class T, class U> void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T> void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) {
wt(' ');
}
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T> void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S> void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i)
wt(' ');
wt(val[i]);
}
}
template <class T> void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i)
wt(' ');
wt(val[i]);
}
}
void print() {
wt('\n');
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
wt(head);
if (sizeof...(Tail))
wt(' ');
print(forward<Tail>(tail)...);
}
void __attribute__((destructor)) _d() {
flush();
}
} // namespace fastio
using fastio::flush;
using fastio::print;
using fastio::read;
inline void first(bool i = true) {
print(i ? "first" : "second");
}
inline void Alice(bool i = true) {
print(i ? "Alice" : "Bob");
}
inline void Takahashi(bool i = true) {
print(i ? "Takahashi" : "Aoki");
}
inline void yes(bool i = true) {
print(i ? "yes" : "no");
}
inline void Yes(bool i = true) {
print(i ? "Yes" : "No");
}
inline void No() {
print("No");
}
inline void YES(bool i = true) {
print(i ? "YES" : "NO");
}
inline void NO() {
print("NO");
}
inline void Yay(bool i = true) {
print(i ? "Yay!" : ":(");
}
inline void Possible(bool i = true) {
print(i ? "Possible" : "Impossible");
}
inline void POSSIBLE(bool i = true) {
print(i ? "POSSIBLE" : "IMPOSSIBLE");
}
/**
* @brief Fast IO
*/
#line 3 "sol.cpp"
#line 2 "library/Math/fastdiv.hpp"
struct FastDiv {
using u64 = unsigned ll;
using u128 = __uint128_t;
u128 mod, mh, ml;
explicit FastDiv(u64 mod = 1) : mod(mod) {
u128 m = u128(-1) / mod;
if (m * mod + mod == u128(0))
++m;
mh = m >> 64;
ml = m & u64(-1);
}
u64 umod() const {
return mod;
}
u64 modulo(u128 x) {
u128 z = (x & u64(-1)) * ml;
z = (x & u64(-1)) * mh + (x >> 64) * ml + (z >> 64);
z = (x >> 64) * mh + (z >> 64);
x -= z * mod;
return x < mod ? x : x - mod;
}
u64 mul(u64 a, u64 b) {
return modulo(u128(a) * b);
}
};
/**
* @brief Fast Division
*/
#line 2 "library/Math/miller.hpp"
struct m64 {
using i64 = int64_t;
using u64 = uint64_t;
using u128 = __uint128_t;
static u64 mod;
static u64 r;
static u64 n2;
static u64 get_r() {
u64 ret = mod;
rep(_,0,5) ret *= 2 - mod * ret;
return ret;
}
static void set_mod(u64 m) {
assert(m < (1LL << 62));
assert((m & 1) == 1);
mod = m;
n2 = -u128(m) % m;
r = get_r();
assert(r * mod == 1);
}
static u64 get_mod() { return mod; }
u64 a;
m64() : a(0) {}
m64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){};
static u64 reduce(const u128 &b) {
return (b + u128(u64(b) * u64(-r)) * mod) >> 64;
}
u64 get() const {
u64 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
m64 &operator*=(const m64 &b) {
a = reduce(u128(a) * b.a);
return *this;
}
m64 operator*(const m64 &b) const { return m64(*this) *= b; }
bool operator==(const m64 &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
bool operator!=(const m64 &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
m64 pow(u128 n) const {
m64 ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
};
typename m64::u64 m64::mod, m64::r, m64::n2;
bool Miller(ll n){
if(n<2 or (n&1)==0)return (n==2);
m64::set_mod(n);
ll d=n-1; while((d&1)==0)d>>=1;
vector<ll> seeds;
if(n<(1<<30))seeds={2, 7, 61};
else seeds={2, 325, 9375, 28178, 450775, 9780504};
for(auto& x:seeds){
if(n<=x)break;
ll t=d;
m64 y=m64(x).pow(t);
while(t!=n-1 and y!=1 and y!=n-1){
y*=y;
t<<=1;
}
if(y!=n-1 and (t&1)==0)return 0;
} return 1;
}
/**
* @brief Miller-Rabin
*/
#line 2 "library/Utility/random.hpp"
namespace Random {
mt19937_64 randgen(chrono::steady_clock::now().time_since_epoch().count());
using u64 = unsigned long long;
u64 get() {
return randgen();
}
template <typename T> T get(T L) { // [0,L]
return get() % (L + 1);
}
template <typename T> T get(T L, T R) { // [L,R]
return get(R - L) + L;
}
double uniform() {
return double(get(1000000000)) / 1000000000;
}
string str(int n) {
string ret;
rep(i, 0, n) ret += get('a', 'z');
return ret;
}
template <typename Iter> void shuffle(Iter first, Iter last) {
if (first == last)
return;
int len = 1;
for (auto it = first + 1; it != last; it++) {
len++;
int j = get(0, len - 1);
if (j != len - 1)
iter_swap(it, first + j);
}
}
template <typename T> vector<T> select(int n, T L, T R) { // [L,R]
if (n * 2 >= R - L + 1) {
vector<T> ret(R - L + 1);
iota(ALL(ret), L);
shuffle(ALL(ret));
ret.resize(n);
return ret;
} else {
unordered_set<T> used;
vector<T> ret;
while (SZ(used) < n) {
T x = get(L, R);
if (!used.count(x)) {
used.insert(x);
ret.push_back(x);
}
}
return ret;
}
}
void relabel(int n, vector<pair<int, int>> &es) {
shuffle(ALL(es));
vector<int> ord(n);
iota(ALL(ord), 0);
shuffle(ALL(ord));
for (auto &[u, v] : es)
u = ord[u], v = ord[v];
}
template <bool directed, bool simple> vector<pair<int, int>> genGraph(int n) {
vector<pair<int, int>> cand, es;
rep(u, 0, n) rep(v, 0, n) {
if (simple and u == v)
continue;
if (!directed and u > v)
continue;
cand.push_back({u, v});
}
int m = get(SZ(cand));
vector<int> ord;
if (simple)
ord = select(m, 0, SZ(cand) - 1);
else {
rep(_, 0, m) ord.push_back(get(SZ(cand) - 1));
}
for (auto &i : ord)
es.push_back(cand[i]);
relabel(n, es);
return es;
}
vector<pair<int, int>> genTree(int n) {
vector<pair<int, int>> es;
rep(i, 1, n) es.push_back({get(i - 1), i});
relabel(n, es);
return es;
}
}; // namespace Random
/**
* @brief Random
*/
#line 4 "library/Math/pollard.hpp"
vector<ll> Pollard(ll n) {
if (n <= 1)
return {};
if (Miller(n))
return {n};
if ((n & 1) == 0) {
vector<ll> v = Pollard(n >> 1);
v.push_back(2);
return v;
}
for (ll x = 2, y = 2, d;;) {
ll c = Random::get(2LL, n - 1);
do {
x = (__int128_t(x) * x + c) % n;
y = (__int128_t(y) * y + c) % n;
y = (__int128_t(y) * y + c) % n;
d = __gcd(x - y + n, n);
} while (d == 1);
if (d < n) {
vector<ll> lb = Pollard(d), rb = Pollard(n / d);
lb.insert(lb.end(), ALL(rb));
return lb;
}
}
}
/**
* @brief Pollard-Rho
*/
#line 4 "library/Math/primitive.hpp"
ll mpow(ll a, i128 t, ll m) {
ll res = 1;
FastDiv im(m);
while (t) {
if (t & 1)
res = im.mul(res, a);
a = im.mul(a, a);
t >>= 1;
}
return res;
}
ll minv(ll a, ll m) {
ll b = m, u = 1, v = 0;
while (b) {
ll t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
u = (u % m + m) % m;
return u;
}
ll getPrimitiveRoot(ll p) {
vector<ll> ps = Pollard(p - 1);
sort(ALL(ps));
rep(x, 1, inf) {
for (auto &q : ps) {
if (mpow(x, (p - 1) / q, p) == 1)
goto fail;
}
return x;
fail:;
}
assert(0);
}
ll extgcd(ll a, ll b, ll &p, ll &q) {
if (b == 0) {
p = 1;
q = 0;
return a;
}
ll d = extgcd(b, a % b, q, p);
q -= a / b * p;
return d;
}
pair<ll, ll> crt(const vector<ll> &vs, const vector<ll> &ms) {
ll V = vs[0], M = ms[0];
rep(i, 1, vs.size()) {
ll p, q, v = vs[i], m = ms[i];
if (M < m)
swap(M, m), swap(V, v);
ll d = extgcd(M, m, p, q);
if ((v - V) % d != 0)
return {0, -1};
ll md = m / d, tmp = (v - V) / d % md * p % md;
V += M * tmp;
M *= md;
}
V = (V % M + M) % M;
return {V, M};
}
ll ModLog(ll a, ll b, ll p) {
ll g = 1;
for (ll t = p; t; t >>= 1)
g = g * a % p;
g = __gcd(g, p);
ll t = 1, c = 0;
for (; t % g; c++) {
if (t == b)
return c;
t = t * a % p;
}
if (b % g)
return -1;
t /= g, b /= g;
ll n = p / g, h = 0, gs = 1;
for (; h * h < n; h++)
gs = gs * a % n;
unordered_map<ll, ll> bs;
for (ll s = 0, e = b; s < h; bs[e] = ++s)
e = e * a % n;
for (ll s = 0, e = t; s < n;) {
e = e * gs % n, s += h;
if (bs.count(e)) {
return c + s - bs[e];
}
}
return -1;
}
ll mod_root(ll k, ll a, ll m) {
if (a == 0)
return k ? 0 : -1;
if (m == 2)
return a & 1;
k %= m - 1;
ll g = gcd(k, m - 1);
if (mpow(a, (m - 1) / g, m) != 1)
return -1;
a = mpow(a, minv(k / g, (m - 1) / g), m);
FastDiv im(m);
auto _subroot = [&](ll p, int e, ll a) -> ll { // x^(p^e)==a(mod m)
ll q = m - 1;
int s = 0;
while (q % p == 0) {
q /= p;
s++;
}
int d = s - e;
ll pe = mpow(p, e, m),
res = mpow(a, ((pe - 1) * minv(q, pe) % pe * q + 1) / pe, m), c = 1;
while (mpow(c, (m - 1) / p, m) == 1)
c++;
c = mpow(c, q, m);
map<ll, ll> mp;
ll v = 1, block = sqrt(d * p) + 1,
bs = mpow(c, mpow(p, s - 1, m - 1) * block % (m - 1), m);
rep(i, 0, block + 1) mp[v] = i, v = im.mul(v, bs);
ll gs = minv(mpow(c, mpow(p, s - 1, m - 1), m), m);
rep(i, 0, d) {
ll err = im.mul(a, minv(mpow(res, pe, m), m));
ll pos = mpow(err, mpow(p, d - 1 - i, m - 1), m);
rep(j, 0, block + 1) {
if (mp.count(pos)) {
res = im.mul(res, mpow(c,
(block * mp[pos] + j) *
mpow(p, i, m - 1) % (m - 1),
m));
break;
}
pos = im.mul(pos, gs);
}
}
return res;
};
for (ll d = 2; d * d <= g; d++)
if (g % d == 0) {
int sz = 0;
while (g % d == 0) {
g /= d;
sz++;
}
a = _subroot(d, sz, a);
}
if (g > 1)
a = _subroot(g, 1, a);
return a;
}
ull floor_root(ull a, ull k) {
if (a <= 1 or k == 1)
return a;
if (k >= 64)
return 1;
if (k == 2)
return sqrtl(a);
constexpr ull LIM = -1;
if (a == LIM)
a--;
auto mul = [&](ull &x, const ull &y) {
if (x <= LIM / y)
x *= y;
else
x = LIM;
};
auto pw = [&](ull x, ull t) -> ull {
ull y = 1;
while (t) {
if (t & 1)
mul(y, x);
mul(x, x);
t >>= 1;
}
return y;
};
ull ret = (k == 3 ? cbrt(a) - 1 : pow(a, nextafter(1 / double(k), 0)));
while (pw(ret + 1, k) <= a)
ret++;
return ret;
}
/**
* @brief Primitive Function
*/
#line 6 "sol.cpp"
#line 2 "library/Convolution/ntt.hpp"
template <typename T> struct NTT {
static constexpr int rank2 = __builtin_ctzll(T::get_mod() - 1);
std::array<T, rank2 + 1> root; // root[i]^(2^i) == 1
std::array<T, rank2 + 1> iroot; // root[i] * iroot[i] == 1
std::array<T, std::max(0, rank2 - 2 + 1)> rate2;
std::array<T, std::max(0, rank2 - 2 + 1)> irate2;
std::array<T, std::max(0, rank2 - 3 + 1)> rate3;
std::array<T, std::max(0, rank2 - 3 + 1)> irate3;
NTT() {
T g = 2;
while (g.pow((T::get_mod() - 1) >> 1) == 1) {
g += 1;
}
root[rank2] = g.pow((T::get_mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
{
T prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 2; i++) {
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
}
{
T prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 3; i++) {
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
}
void ntt(std::vector<T> &a, bool type = 0) {
int n = int(a.size());
int h = __builtin_ctzll((unsigned int)n);
a.resize(1 << h);
if (type) {
int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len) {
if (len == 1) {
int p = 1 << (h - len);
T irot = 1;
for (int s = 0; s < (1 << (len - 1)); s++) {
int offset = s << (h - len + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(T::get_mod() + l.v - r.v) *
irot.v;
;
}
if (s + 1 != (1 << (len - 1)))
irot *= irate2[__builtin_ctzll(~(unsigned int)(s))];
}
len--;
} else {
// 4-base
int p = 1 << (h - len);
T irot = 1, iimag = iroot[2];
for (int s = 0; s < (1 << (len - 2)); s++) {
T irot2 = irot * irot;
T irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
auto a0 = 1ULL * a[i + offset + 0 * p].v;
auto a1 = 1ULL * a[i + offset + 1 * p].v;
auto a2 = 1ULL * a[i + offset + 2 * p].v;
auto a3 = 1ULL * a[i + offset + 3 * p].v;
auto a2na3iimag =
1ULL * T((T::get_mod() + a2 - a3) * iimag.v).v;
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] =
(a0 + (T::get_mod() - a1) + a2na3iimag) *
irot.v;
a[i + offset + 2 * p] =
(a0 + a1 + (T::get_mod() - a2) +
(T::get_mod() - a3)) *
irot2.v;
a[i + offset + 3 * p] =
(a0 + (T::get_mod() - a1) +
(T::get_mod() - a2na3iimag)) *
irot3.v;
}
if (s + 1 != (1 << (len - 2)))
irot *= irate3[__builtin_ctzll(~(unsigned int)(s))];
}
len -= 2;
}
}
T e = T(n).inv();
for (auto &x : a)
x *= e;
} else {
int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
T rot = 1;
for (int s = 0; s < (1 << len); s++) {
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
if (s + 1 != (1 << len))
rot *= rate2[__builtin_ctzll(~(unsigned int)(s))];
}
len++;
} else {
// 4-base
int p = 1 << (h - len - 2);
T rot = 1, imag = root[2];
for (int s = 0; s < (1 << len); s++) {
T rot2 = rot * rot;
T rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto mod2 = 1ULL * T::get_mod() * T::get_mod();
auto a0 = 1ULL * a[i + offset].v;
auto a1 = 1ULL * a[i + offset + p].v * rot.v;
auto a2 = 1ULL * a[i + offset + 2 * p].v * rot2.v;
auto a3 = 1ULL * a[i + offset + 3 * p].v * rot3.v;
auto a1na3imag =
1ULL * T(a1 + mod2 - a3).v * imag.v;
auto na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] =
a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] =
a0 + na2 + (mod2 - a1na3imag);
}
if (s + 1 != (1 << len))
rot *= rate3[__builtin_ctzll(~(unsigned int)(s))];
}
len += 2;
}
}
}
}
vector<T> mult(const vector<T> &a, const vector<T> &b) {
if (a.empty() or b.empty())
return vector<T>();
int as = a.size(), bs = b.size();
int n = as + bs - 1;
if (as <= 30 or bs <= 30) {
if (as > 30)
return mult(b, a);
vector<T> res(n);
rep(i, 0, as) rep(j, 0, bs) res[i + j] += a[i] * b[j];
return res;
}
int m = 1;
while (m < n)
m <<= 1;
vector<T> res(m);
rep(i, 0, as) res[i] = a[i];
ntt(res);
if (a == b)
rep(i, 0, m) res[i] *= res[i];
else {
vector<T> c(m);
rep(i, 0, bs) c[i] = b[i];
ntt(c);
rep(i, 0, m) res[i] *= c[i];
}
ntt(res, 1);
res.resize(n);
return res;
}
};
/**
* @brief Number Theoretic Transform
*/
#line 2 "library/Math/modint.hpp"
template <unsigned mod = 1000000007> struct fp {
unsigned v;
static constexpr int get_mod() {
return mod;
}
constexpr unsigned inv() const {
assert(v != 0);
int x = v, y = mod, p = 1, q = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, p -= t * q;
tmp = x, x = y, y = tmp;
tmp = p, p = q, q = tmp;
}
if (p < 0)
p += mod;
return p;
}
constexpr fp(ll x = 0) : v(x >= 0 ? x % mod : (mod - (-x) % mod) % mod) {}
fp operator-() const {
return fp() - *this;
}
fp pow(ull t) {
fp res = 1, b = *this;
while (t) {
if (t & 1)
res *= b;
b *= b;
t >>= 1;
}
return res;
}
fp &operator+=(const fp &x) {
if ((v += x.v) >= mod)
v -= mod;
return *this;
}
fp &operator-=(const fp &x) {
if ((v += mod - x.v) >= mod)
v -= mod;
return *this;
}
fp &operator*=(const fp &x) {
v = ull(v) * x.v % mod;
return *this;
}
fp &operator/=(const fp &x) {
v = ull(v) * x.inv() % mod;
return *this;
}
fp operator+(const fp &x) const {
return fp(*this) += x;
}
fp operator-(const fp &x) const {
return fp(*this) -= x;
}
fp operator*(const fp &x) const {
return fp(*this) *= x;
}
fp operator/(const fp &x) const {
return fp(*this) /= x;
}
bool operator==(const fp &x) const {
return v == x.v;
}
bool operator!=(const fp &x) const {
return v != x.v;
}
friend istream &operator>>(istream &is, fp &x) {
return is >> x.v;
}
friend ostream &operator<<(ostream &os, const fp &x) {
return os << x.v;
}
};
template <unsigned mod> void rd(fp<mod> &x) {
fastio::rd(x.v);
}
template <unsigned mod> void wt(fp<mod> x) {
fastio::wt(x.v);
}
/**
* @brief Modint
*/
#line 4 "library/Convolution/arbitrary.hpp"
using M1 = fp<1045430273>;
using M2 = fp<1051721729>;
using M3 = fp<1053818881>;
NTT<M1> N1;
NTT<M2> N2;
NTT<M3> N3;
constexpr int r_12 = M2(M1::get_mod()).inv();
constexpr int r_13 = M3(M1::get_mod()).inv();
constexpr int r_23 = M3(M2::get_mod()).inv();
constexpr int r_1323 = M3(ll(r_13) * r_23).v;
constexpr ll w1 = M1::get_mod();
constexpr ll w2 = ll(w1) * M2::get_mod();
template <typename T>
vector<T> ArbitraryMult(const vector<int> &a, const vector<int> &b) {
if (a.empty() or b.empty())
return vector<T>();
int n = a.size() + b.size() - 1;
vector<T> res(n);
if (min(a.size(), b.size()) <= 60) {
rep(i, 0, a.size()) rep(j, 0, b.size()) res[i + j] += T(a[i]) * b[j];
return res;
}
vector<int> vals[3];
vector<M1> a1(ALL(a)), b1(ALL(b)), c1 = N1.mult(a1, b1);
vector<M2> a2(ALL(a)), b2(ALL(b)), c2 = N2.mult(a2, b2);
vector<M3> a3(ALL(a)), b3(ALL(b)), c3 = N3.mult(a3, b3);
for (M1 x : c1)
vals[0].push_back(x.v);
for (M2 x : c2)
vals[1].push_back(x.v);
for (M3 x : c3)
vals[2].push_back(x.v);
rep(i, 0, n) {
ll p = vals[0][i];
ll q = (vals[1][i] + M2::get_mod() - p) * r_12 % M2::get_mod();
ll r = ((vals[2][i] + M3::get_mod() - p) * r_1323 +
(M3::get_mod() - q) * r_23) %
M3::get_mod();
res[i] = (T(r) * w2 + q * w1 + p);
}
return res;
}
template <typename T>
vector<T> ArbitraryMult(const vector<T> &a, const vector<T> &b) {
vector<int> A, B;
for (auto &x : a)
A.push_back(x.v);
for (auto &x : b)
B.push_back(x.v);
return ArbitraryMult<T>(A, B);
}
/**
* @brief Arbitrary Mod Convolution
*/
#line 3 "library/Math/bigint.hpp"
template <int D> struct bigint {
using u128 = __uint128_t;
static const int B = pow(10, D);
int sign = 0;
vector<int> v;
static int get_D() { return D; }
static int get_B() { return B; }
bigint() {}
bigint(const vector<int> &_v, bool _s = false) : sign(_s), v(_v) {}
bigint(ll x) {
if (x < 0)
x *= -1, sign = 1;
while (x) {
v.push_back(x % B);
x /= B;
}
}
bigint(string s) {
if (s[0] == '-')
s.erase(s.begin()), sign = 1;
int add = 0, cnt = 0, base = 1;
while (s.size()) {
if (cnt == D) {
v.push_back(add);
cnt = 0;
add = 0;
base = 1;
}
add = (s.back() - '0') * base + add;
cnt++;
base *= 10;
s.pop_back();
}
if (add)
v.push_back(add);
}
bigint operator-() const {
bigint res = *this;
res.sign ^= 1;
return res;
}
bigint abs() const {
bigint res = *this;
res.sign = 0;
return res;
}
int &operator[](const int i) { return v[i]; }
int size() const { return v.size(); }
void norm() {
rep(i, 0, v.size() - 1) {
if (v[i] >= 0) {
v[i + 1] += v[i] / B;
v[i] %= B;
} else {
int c = (-v[i] + B - 1) / B;
v[i] += c * B;
v[i + 1] -= c;
}
}
while (!v.empty() and v.back() >= B) {
int c = v.back() / B;
v.back() %= B;
v.push_back(c);
}
while (!v.empty() and v.back() == 0)
v.pop_back();
}
string to_str() const {
string res;
if (v.empty())
return "0";
if (sign)
res += '-';
res += to_string(v.back());
for (int i = v.size() - 2; i >= 0; i--) {
string add;
int w = v[i];
rep(_, 0, D) {
add += ('0' + (w % 10));
w /= 10;
}
reverse(ALL(add));
res += add;
}
return res;
}
friend istream &operator>>(istream &is, bigint<D> &x) {
string tmp;
is >> tmp;
x = bigint(tmp);
return is;
}
friend ostream &operator<<(ostream &os, bigint<D> x) {
os << x.to_str();
return os;
}
bigint &operator<<=(const int &x) {
if (!v.empty()) {
vector<int> add(x, 0);
v.insert(v.begin(), ALL(add));
}
return *this;
}
bigint &operator>>=(const int &x) {
v = vector<int>(v.begin() + min(x, (int)v.size()), v.end());
return *this;
}
bigint &operator+=(const bigint &x) {
if (sign != x.sign) {
*this -= (-x);
return *this;
}
if ((int)v.size() < (int)x.size())
v.resize(x.size(), 0);
rep(i, 0, x.size()) { v[i] += x.v[i]; }
norm();
return *this;
}
bigint &operator-=(const bigint &x) {
if (sign != x.sign) {
*this += (-x);
return *this;
}
if (abs() < x.abs()) {
*this = x - (*this);
sign ^= 1;
return *this;
}
rep(i, 0, x.size()) { v[i] -= x.v[i]; }
norm();
return *this;
}
bigint &operator*=(const bigint &x) {
sign ^= x.sign;
auto v1 = ArbitraryMult<u128>(v, x.v);
u128 add = 0;
v.clear();
v.reserve(v1.size() + 3);
for (int i = 0;; i++) {
if (i >= int(v1.size()) and add == 0)
break;
if (i < int(v1.size()))
add += v1[i];
v.push_back(add % B);
add /= B;
}
norm();
return *this;
}
bigint div_naive(const bigint &a, const bigint &b) {
if (SZ(b) == 1)
return a.div(b.v.back());
if (a < b)
return bigint();
int norm = B / (b.v.back() + 1);
bigint x = a.mul(norm), y = b.mul(norm);
int yb = y.v.back();
bigint quo, rem;
quo.v.resize(x.size() - y.size() + 1);
rem.v = {x.v.end() - y.size(), x.v.end()};
for (int i = x.size() - y.size(); i >= 0; i--) {
if (rem.size() == y.size()) {
if (rem >= y) {
quo[i] = 1;
rem -= y;
}
} else if (rem.size() > y.size()) {
ll rb = ll(rem.v.back()) * B + rem[rem.size() - 2];
int q = rb / yb;
bigint yq = y.mul(q);
while (rem < yq) {
q--;
yq -= y;
}
rem -= yq;
while (rem >= y) {
q++;
rem -= y;
}
quo[i] = q;
}
if (i)
rem.v.insert(rem.v.begin(), x[i - 1]);
}
return quo;
}
bigint &operator/=(const bigint &x) {
bigint a = abs(), b = x.abs();
sign ^= x.sign;
if (a < b)
return *this = bigint();
if (b.size() == 1)
return *this = a.div(b.v.back());
int deg = a.size() - b.size() + 2, k = deg;
while (k > 64)
k = (k + 1) >> 1;
bigint base(1);
base <<= (b.size() + k);
bigint inv(div_naive(base, b));
while (k < deg) {
bigint y = inv.square();
y.v.insert(y.v.begin(), 0);
int l = min(SZ(b), k * 2 + 1);
bigint pref;
pref.v = {b.v.end() - l, b.v.end()};
y *= pref;
y >>= l;
inv = inv + inv;
inv <<= k + 1;
inv -= y;
inv.v.erase(inv.v.begin());
k <<= 1;
}
inv >>= (k - deg);
(*this) = a * inv;
(*this) >>= int(a.size() + 2);
bigint mul = (*this) * b;
while (mul + b <= a) {
(*this) += bigint(1);
mul += b;
}
while (mul > a) {
(*this) -= bigint(1);
mul -= b;
}
return *this;
}
bigint &operator%=(const bigint &x) {
bigint div = (*this) / x;
(*this) -= div * x;
return *this;
}
bigint square() const {
bigint ret;
auto v1 = ArbitraryMult<u128>(v, v);
u128 add = 0;
ret.v.reserve(v1.size() + 3);
for (int i = 0;; i++) {
if (i >= int(v1.size()) and add == 0)
break;
if (i < int(v1.size()))
add += v1[i];
ret.v.push_back(add % B);
add /= B;
}
return ret;
}
bigint mul(ll x) const {
bigint res;
if (x < 0)
res.sign ^= 1, x *= -1;
u128 add = 0;
res.v.reserve(v.size() + 3);
for (int i = 0;; i++) {
if (i >= int(v.size()) and add == 0)
break;
if (i < int(v.size()))
add += ll(v[i]) * x;
res.v.push_back(add % B);
add /= B;
}
return res;
}
bigint div(ll x) const {
bigint res = *this;
if (x < 0)
res.sign ^= 1, x *= -1;
ll add = 0;
for (int i = res.v.size() - 1; i >= 0; i--) {
add = add * B + res.v[i];
int q = add / x, r = add % x;
res.v[i] = q, add = r;
}
res.norm();
return res;
}
bigint operator<<(const int &x) const { return bigint(*this) <<= x; }
bigint operator>>(const int &x) const { return bigint(*this) >>= x; }
bigint operator+(const bigint &x) const { return bigint(*this) += x; }
bigint operator-(const bigint &x) const { return bigint(*this) -= x; }
bigint operator*(const bigint &x) const { return bigint(*this) *= x; }
bigint operator/(const bigint &x) const { return bigint(*this) /= x; }
bigint operator%(const bigint &x) const { return bigint(*this) %= x; }
bool operator<(const bigint &x) const {
if (sign != x.sign)
return sign > x.sign;
if ((int)v.size() != (int)x.size()) {
if (sign)
return (int)x.size() < (int)v.size();
else
return (int)v.size() < (int)x.size();
}
for (int i = v.size() - 1; i >= 0; i--)
if (v[i] != x.v[i]) {
if (sign)
return x.v[i] < v[i];
else
return v[i] < x.v[i];
}
return false;
}
bool operator>(const bigint &x) const { return x < *this; }
bool operator<=(const bigint &x) const { return !(*this > x); }
bool operator>=(const bigint &x) const { return !(*this < x); }
bool operator==(const bigint &x) const {
return !(*this < x) and !(*this > x);
}
bool operator!=(const bigint &x) const { return !(*this == x); }
};
typedef bigint<9> Bigint;
struct Bigfloat {
Bigint v;
int p = 0;
Bigfloat() {}
Bigfloat(const ll &_v) { v = Bigint(_v); }
Bigfloat(const Bigint &_v, int _p = 0) : v(_v), p(_p) {}
void set(int _p) {
if (p < _p) {
v >>= (_p - p);
} else {
v <<= (p - _p);
}
p = _p;
}
Bigint to_int() const {
if (p < 0)
return v >> (-p);
else
return v << p;
}
Bigfloat &operator+=(const Bigfloat &x) {
if (p > x.p)
set(x.p), v += x.v;
else
v += x.v << (x.p - p);
return *this;
}
Bigfloat &operator-=(const Bigfloat &x) {
if (p > x.p)
set(x.p), v -= x.v;
else
v -= x.v << (x.p - p);
return *this;
}
Bigfloat square() {
Bigfloat res = *this;
res.p *= 2;
res.v = res.v.square();
return res;
}
Bigfloat mul(ll x) {
Bigfloat res = *this;
res.v = v.mul(x);
return res;
}
Bigfloat div(ll x) {
Bigfloat res = *this;
res.v = v.div(x);
return res;
}
Bigfloat &operator*=(const Bigfloat &x) {
p += x.p;
v *= x.v;
return *this;
}
Bigfloat &operator/=(const Bigfloat &x) {
p -= x.p;
v /= x.v;
return *this;
}
Bigfloat operator+(const Bigfloat &x) const { return Bigfloat(*this) += x; }
Bigfloat operator-(const Bigfloat &x) const { return Bigfloat(*this) -= x; }
Bigfloat operator*(const Bigfloat &x) const { return Bigfloat(*this) *= x; }
Bigfloat operator/(const Bigfloat &x) const { return Bigfloat(*this) /= x; }
string to_str() {
string res = v.abs().to_str();
int d = Bigint::get_D();
if (p * d > 0)
res += string(p * d, '0');
else if (-p * d >= 1 and -p * d < (int)res.size()) {
res = res.substr(0, (int)res.size() + p * d) + '.' +
res.substr((int)res.size() + p * d);
} else if (-p * d >= (int)res.size())
res = "0." + string(-p * d - (int)res.size(), '0') + res;
if (v.sign) {
res.insert(res.begin(), '-');
}
return res;
}
friend ostream &operator<<(ostream &os, Bigfloat x) {
os << x.to_str();
return os;
}
};
Bigfloat sqrt(ll n, int d) {
Bigfloat res(Bigint((ll)sqrt(1LL * Bigint::get_B() * Bigint::get_B() / n)),
-1),
pre;
int cur = 1;
while (pre.v != res.v) {
cur = min(cur << 1, d);
pre = res;
Bigfloat add = Bigfloat(1) - res.square().mul(n);
add.set(-cur);
res += (res * add).div(2);
res.set(-cur);
}
return res.mul(n);
}
/**
* @brief Big Integer(Float)
*/
#line 8 "sol.cpp"
Bigint Mpow(Bigint a, Bigint t, Bigint m) {
Bigint ret = 1;
while (t != 0) {
if (t % 2 == 1)
ret = (ret * a) % m;
a = (a * a) % m;
t /= 2;
}
return ret;
}
void solve(int _rot) {
// print("Case #"+to_string(_rot)+":");
ll B, N, M;
read(B, N, M);
if (gcd(B, M) != 1) {
print(-1);
return;
}
ll M2 = M % B;
ll inv = minv(M2, B);
ll ord = ModLog(M2, inv, B) + 1;
auto ps = Pollard(ord);
UNIQUE(ps);
bool ch = 0;
for (auto &p : ps)
if (B % p != 0) {
ch = 1;
break;
}
if (ch) {
print(-1);
return;
}
if (N == 0) {
print(0);
return;
}
{
ll n = N * 2 + 10;
Bigint Bn = 1, BnN = 1;
rep(_, 0, n) Bn *= B;
rep(_, 0, n + N) BnN *= B;
Bigint mpw = Mpow(M, Bn, BnN);
Bigint a = (mpw - 1) / Bn;
print(a.to_str());
}
}
int main() {
int t;
read(t);
rep(rot, 0, t) solve(rot + 1);
return 0;
}