結果
| 問題 | No.2440 Accuracy of Integer Division Approximate Functions |
| ユーザー |
 maspy
|
| 提出日時 | 2023-11-10 22:46:51 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 203 ms / 2,000 ms |
| コード長 | 40,253 bytes |
| コンパイル時間 | 8,532 ms |
| コンパイル使用メモリ | 343,120 KB |
| 実行使用メモリ | 5,376 KB |
| 最終ジャッジ日時 | 2024-09-26 02:00:31 |
| 合計ジャッジ時間 | 12,826 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 184 ms
5,376 KB |
| testcase_02 | AC | 183 ms
5,376 KB |
| testcase_03 | AC | 187 ms
5,376 KB |
| testcase_04 | AC | 186 ms
5,376 KB |
| testcase_05 | AC | 181 ms
5,376 KB |
| testcase_06 | AC | 197 ms
5,376 KB |
| testcase_07 | AC | 200 ms
5,376 KB |
| testcase_08 | AC | 203 ms
5,376 KB |
| testcase_09 | AC | 202 ms
5,376 KB |
| testcase_10 | AC | 198 ms
5,376 KB |
| testcase_11 | AC | 183 ms
5,376 KB |
| testcase_12 | AC | 184 ms
5,376 KB |
| testcase_13 | AC | 186 ms
5,376 KB |
| testcase_14 | AC | 182 ms
5,376 KB |
| testcase_15 | AC | 185 ms
5,376 KB |
| testcase_16 | AC | 183 ms
5,376 KB |
| testcase_17 | AC | 182 ms
5,376 KB |
| testcase_18 | AC | 184 ms
5,376 KB |
| testcase_19 | AC | 184 ms
5,376 KB |
| testcase_20 | AC | 185 ms
5,376 KB |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
#define FASTIO
#include <unistd.h>
// https://judge.yosupo.jp/submission/21623
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() {
memcpy(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(u32 &x) { rd_integer(x); }
void rd(u64 &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); }
void rd(f128 &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(vc<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(u32 x) { wt_integer(x); }
void wt(u64 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); }
void wt(f128 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)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"
#line 2 "/home/maspy/compro/library/mod/floor_sum_of_linear.hpp"
// sum_{x in [L,R)} floor(ax + b, mod)
// I は範囲内で ax+b がオーバーフローしない程度
template <typename O = i128, typename I = long long>
O floor_sum_of_linear(I L, I R, I a, I b, I mod) {
assert(L <= R);
O res = 0;
b += L * a;
I N = R - L;
if (b < 0) {
I k = ceil(-b, mod);
b += k * mod;
res -= O(N) * O(k);
}
while (N) {
I q;
tie(q, a) = divmod(a, mod);
res += (N & 1 ? O(N) * O((N - 1) / 2) * O(q) : O(N / 2) * O(N - 1) * O(q));
if (b >= mod) {
tie(q, b) = divmod(b, mod);
res += O(N) * q;
}
tie(N, b) = divmod(a * N + b, mod);
tie(a, mod) = mp(mod, a);
}
return res;
}
#line 2 "/home/maspy/compro/library/mod/modint_common.hpp"
struct has_mod_impl {
template <class T>
static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};
template <typename mint>
mint inv(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {0, 1};
assert(0 <= n);
if (n >= mod) n %= mod;
while (len(dat) <= n) {
int k = len(dat);
int q = (mod + k - 1) / k;
dat.eb(dat[k * q - mod] * mint::raw(q));
}
return dat[n];
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
assert(0 <= n && n < mod);
static vector<mint> dat = {1, 1};
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
static vector<mint> dat = {1, 1};
if (n < 0) return mint(0);
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
return dat[n];
}
template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
return (mint(1) * ... * fact_inv<mint>(xs));
}
template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}
template <typename mint>
mint C_dense(int n, int k) {
static vvc<mint> C;
static int H = 0, W = 0;
auto calc = [&](int i, int j) -> mint {
if (i == 0) return (j == 0 ? mint(1) : mint(0));
return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
};
if (W <= k) {
FOR(i, H) {
C[i].resize(k + 1);
FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
}
W = k + 1;
}
if (H <= n) {
C.resize(n + 1);
FOR(i, H, n + 1) {
C[i].resize(W);
FOR(j, W) { C[i][j] = calc(i, j); }
}
H = n + 1;
}
return C[n][k];
}
template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
if constexpr (dense) return C_dense<mint>(n, k);
if constexpr (!large) return multinomial<mint>(n, k, n - k);
k = min(k, n - k);
mint x(1);
FOR(i, k) x *= mint(n - i);
return x * fact_inv<mint>(k);
}
template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
assert(n >= 0);
assert(0 <= k && k <= n);
if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
return mint(1) / C<mint, 1>(n, k);
}
// [x^d](1-x)^{-n}
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
assert(n >= 0);
if (d < 0) return mint(0);
if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
return C<mint, large, dense>(n + d - 1, d);
}
#line 3 "/home/maspy/compro/library/mod/modint.hpp"
template <int mod>
struct modint {
static constexpr u32 umod = u32(mod);
static_assert(umod < u32(1) << 31);
u32 val;
static modint raw(u32 v) {
modint x;
x.val = v;
return x;
}
constexpr modint() : val(0) {}
constexpr modint(u32 x) : val(x % umod) {}
constexpr modint(u64 x) : val(x % umod) {}
constexpr modint(u128 x) : val(x % umod) {}
constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};
bool operator<(const modint &other) const { return val < other.val; }
modint &operator+=(const modint &p) {
if ((val += p.val) >= umod) val -= umod;
return *this;
}
modint &operator-=(const modint &p) {
if ((val += umod - p.val) >= umod) val -= umod;
return *this;
}
modint &operator*=(const modint &p) {
val = u64(val) * p.val % umod;
return *this;
}
modint &operator/=(const modint &p) {
*this *= p.inverse();
return *this;
}
modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
modint operator+(const modint &p) const { return modint(*this) += p; }
modint operator-(const modint &p) const { return modint(*this) -= p; }
modint operator*(const modint &p) const { return modint(*this) *= p; }
modint operator/(const modint &p) const { return modint(*this) /= p; }
bool operator==(const modint &p) const { return val == p.val; }
bool operator!=(const modint &p) const { return val != p.val; }
modint inverse() const {
int a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return modint(u);
}
modint pow(ll n) const {
assert(n >= 0);
modint ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
static constexpr int get_mod() { return mod; }
// (n, r), r は 1 の 2^n 乗根
static constexpr pair<int, int> ntt_info() {
if (mod == 167772161) return {25, 17};
if (mod == 469762049) return {26, 30};
if (mod == 754974721) return {24, 362};
if (mod == 880803841) return {23, 211};
if (mod == 943718401) return {22, 663003469};
if (mod == 998244353) return {23, 31};
if (mod == 1045430273) return {20, 363};
if (mod == 1051721729) return {20, 330};
if (mod == 1053818881) return {20, 2789};
return {-1, -1};
}
static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};
#ifdef FASTIO
template <int mod>
void rd(modint<mod> &x) {
fastio::rd(x.val);
assert(0 <= x.val && x.val < mod);
}
template <int mod>
void wt(modint<mod> x) {
fastio::wt(x.val);
}
#endif
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 2 "/home/maspy/compro/library/mod/mod_inv.hpp"
// long でも大丈夫
// (val * x - 1) が mod の倍数になるようにする
// 特に mod=0 なら x=0 が満たす
ll mod_inv(ll val, ll mod) {
if (mod == 0) return 0;
mod = abs(mod);
val %= mod;
if (val < 0) val += mod;
ll a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
if (u < 0) u += mod;
return u;
}
#line 1 "/home/maspy/compro/library/mod/crt3.hpp"
constexpr u32 mod_pow_constexpr(u64 a, u64 n, u32 mod) {
a %= mod;
u64 res = 1;
FOR(32) {
if (n & 1) res = res * a % mod;
a = a * a % mod, n /= 2;
}
return res;
}
template <typename T, u32 p0, u32 p1, u32 p2>
T CRT3(u64 a0, u64 a1, u64 a2) {
static_assert(p0 < p1 && p1 < p2);
static constexpr u64 x0_1 = mod_pow_constexpr(p0, p1 - 2, p1);
static constexpr u64 x01_2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);
u64 c = (a1 - a0 + p1) * x0_1 % p1;
u64 a = a0 + c * p0;
c = (a2 - a % p2 + p2) * x01_2 % p2;
return T(a) + T(c) * T(p0) * T(p1);
}
#line 2 "/home/maspy/compro/library/poly/convolution_naive.hpp"
template <class T, typename enable_if<!has_mod<T>::value>::type* = nullptr>
vc<T> convolution_naive(const vc<T>& a, const vc<T>& b) {
int n = int(a.size()), m = int(b.size());
if (n > m) return convolution_naive<T>(b, a);
if (n == 0) return {};
vector<T> ans(n + m - 1);
FOR(i, n) FOR(j, m) ans[i + j] += a[i] * b[j];
return ans;
}
template <class T, typename enable_if<has_mod<T>::value>::type* = nullptr>
vc<T> convolution_naive(const vc<T>& a, const vc<T>& b) {
int n = int(a.size()), m = int(b.size());
if (n > m) return convolution_naive<T>(b, a);
if (n == 0) return {};
vc<T> ans(n + m - 1);
if (n <= 16 && (T::get_mod() < (1 << 30))) {
for (int k = 0; k < n + m - 1; ++k) {
int s = max(0, k - m + 1);
int t = min(n, k + 1);
u64 sm = 0;
for (int i = s; i < t; ++i) { sm += u64(a[i].val) * (b[k - i].val); }
ans[k] = sm;
}
} else {
for (int k = 0; k < n + m - 1; ++k) {
int s = max(0, k - m + 1);
int t = min(n, k + 1);
u128 sm = 0;
for (int i = s; i < t; ++i) { sm += u64(a[i].val) * (b[k - i].val); }
ans[k] = T::raw(sm % T::get_mod());
}
}
return ans;
}
#line 2 "/home/maspy/compro/library/poly/convolution_karatsuba.hpp"
// 任意の環でできる
template <typename T>
vc<T> convolution_karatsuba(const vc<T>& f, const vc<T>& g) {
const int thresh = 30;
if (min(len(f), len(g)) <= thresh) return convolution_naive(f, g);
int n = max(len(f), len(g));
int m = ceil(n, 2);
vc<T> f1, f2, g1, g2;
if (len(f) < m) f1 = f;
if (len(f) >= m) f1 = {f.begin(), f.begin() + m};
if (len(f) >= m) f2 = {f.begin() + m, f.end()};
if (len(g) < m) g1 = g;
if (len(g) >= m) g1 = {g.begin(), g.begin() + m};
if (len(g) >= m) g2 = {g.begin() + m, g.end()};
vc<T> a = convolution_karatsuba(f1, g1);
vc<T> b = convolution_karatsuba(f2, g2);
FOR(i, len(f2)) f1[i] += f2[i];
FOR(i, len(g2)) g1[i] += g2[i];
vc<T> c = convolution_karatsuba(f1, g1);
vc<T> F(len(f) + len(g) - 1);
assert(2 * m + len(b) <= len(F));
FOR(i, len(a)) F[i] += a[i], c[i] -= a[i];
FOR(i, len(b)) F[2 * m + i] += b[i], c[i] -= b[i];
if (c.back() == T(0)) c.pop_back();
FOR(i, len(c)) if (c[i] != T(0)) F[m + i] += c[i];
return F;
}
#line 2 "/home/maspy/compro/library/poly/ntt.hpp"
template <class mint>
void ntt(vector<mint>& a, bool inverse) {
assert(mint::can_ntt());
const int rank2 = mint::ntt_info().fi;
const int mod = mint::get_mod();
static array<mint, 30> root, iroot;
static array<mint, 30> rate2, irate2;
static array<mint, 30> rate3, irate3;
static bool prepared = 0;
if (!prepared) {
prepared = 1;
root[rank2] = mint::ntt_info().se;
iroot[rank2] = mint(1) / root[rank2];
FOR_R(i, rank2) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
mint 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];
}
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];
}
}
int n = int(a.size());
int h = topbit(n);
assert(n == 1 << h);
if (!inverse) {
int len = 0;
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
mint rot = 1;
FOR(s, 1 << len) {
int offset = s << (h - len);
FOR(i, p) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
rot *= rate2[topbit(~s & -~s)];
}
len++;
} else {
int p = 1 << (h - len - 2);
mint rot = 1, imag = root[2];
for (int s = 0; s < (1 << len); s++) {
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
u64 mod2 = u64(mod) * mod;
u64 a0 = a[i + offset].val;
u64 a1 = u64(a[i + offset + p].val) * rot.val;
u64 a2 = u64(a[i + offset + 2 * p].val) * rot2.val;
u64 a3 = u64(a[i + offset + 3 * p].val) * rot3.val;
u64 a1na3imag = (a1 + mod2 - a3) % mod * imag.val;
u64 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);
}
rot *= rate3[topbit(~s & -~s)];
}
len += 2;
}
}
} else {
mint coef = mint(1) / mint(len(a));
FOR(i, len(a)) a[i] *= coef;
int len = h;
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
FOR(s, 1 << (len - 1)) {
int offset = s << (h - len + 1);
FOR(i, p) {
u64 l = a[i + offset].val;
u64 r = a[i + offset + p].val;
a[i + offset] = l + r;
a[i + offset + p] = (mod + l - r) * irot.val;
}
irot *= irate2[topbit(~s & -~s)];
}
len--;
} else {
int p = 1 << (h - len);
mint irot = 1, iimag = iroot[2];
FOR(s, (1 << (len - 2))) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
u64 a0 = a[i + offset + 0 * p].val;
u64 a1 = a[i + offset + 1 * p].val;
u64 a2 = a[i + offset + 2 * p].val;
u64 a3 = a[i + offset + 3 * p].val;
u64 x = (mod + a2 - a3) * iimag.val % mod;
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] = (a0 + mod - a1 + x) * irot.val;
a[i + offset + 2 * p] = (a0 + a1 + 2 * mod - a2 - a3) * irot2.val;
a[i + offset + 3 * p] = (a0 + 2 * mod - a1 - x) * irot3.val;
}
irot *= irate3[topbit(~s & -~s)];
}
len -= 2;
}
}
}
}
#line 1 "/home/maspy/compro/library/poly/fft.hpp"
namespace CFFT {
using real = double;
struct C {
real x, y;
C() : x(0), y(0) {}
C(real x, real y) : x(x), y(y) {}
inline C operator+(const C& c) const { return C(x + c.x, y + c.y); }
inline C operator-(const C& c) const { return C(x - c.x, y - c.y); }
inline C operator*(const C& c) const {
return C(x * c.x - y * c.y, x * c.y + y * c.x);
}
inline C conj() const { return C(x, -y); }
};
const real PI = acosl(-1);
int base = 1;
vector<C> rts = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};
void ensure_base(int nbase) {
if (nbase <= base) return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for (int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
while (base < nbase) {
real angle = PI * 2.0 / (1 << (base + 1));
for (int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
real angle_i = angle * (2 * i + 1 - (1 << base));
rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
}
++base;
}
}
void fft(vector<C>& a, int n) {
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for (int i = 0; i < n; i++) {
if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); }
}
for (int k = 1; k < n; k <<= 1) {
for (int i = 0; i < n; i += 2 * k) {
for (int j = 0; j < k; j++) {
C z = a[i + j + k] * rts[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
} // namespace CFFT
#line 9 "/home/maspy/compro/library/poly/convolution.hpp"
template <class mint>
vector<mint> convolution_ntt(vector<mint> a, vector<mint> b) {
if (a.empty() || b.empty()) return {};
int n = int(a.size()), m = int(b.size());
int sz = 1;
while (sz < n + m - 1) sz *= 2;
// sz = 2^k のときの高速化。分割統治的なやつで損しまくるので。
if ((n + m - 3) <= sz / 2) {
auto a_last = a.back(), b_last = b.back();
a.pop_back(), b.pop_back();
auto c = convolution(a, b);
c.resize(n + m - 1);
c[n + m - 2] = a_last * b_last;
FOR(i, len(a)) c[i + len(b)] += a[i] * b_last;
FOR(i, len(b)) c[i + len(a)] += b[i] * a_last;
return c;
}
a.resize(sz), b.resize(sz);
bool same = a == b;
ntt(a, 0);
if (same) {
b = a;
} else {
ntt(b, 0);
}
FOR(i, sz) a[i] *= b[i];
ntt(a, 1);
a.resize(n + m - 1);
return a;
}
template <typename mint>
vector<mint> convolution_garner(const vector<mint>& a, const vector<mint>& b) {
int n = len(a), m = len(b);
if (!n || !m) return {};
static constexpr int p0 = 167772161;
static constexpr int p1 = 469762049;
static constexpr int p2 = 754974721;
using mint0 = modint<p0>;
using mint1 = modint<p1>;
using mint2 = modint<p2>;
vc<mint0> a0(n), b0(m);
vc<mint1> a1(n), b1(m);
vc<mint2> a2(n), b2(m);
FOR(i, n) a0[i] = a[i].val, a1[i] = a[i].val, a2[i] = a[i].val;
FOR(i, m) b0[i] = b[i].val, b1[i] = b[i].val, b2[i] = b[i].val;
auto c0 = convolution_ntt<mint0>(a0, b0);
auto c1 = convolution_ntt<mint1>(a1, b1);
auto c2 = convolution_ntt<mint2>(a2, b2);
vc<mint> c(len(c0));
FOR(i, n + m - 1) {
c[i] = CRT3<mint, p0, p1, p2>(c0[i].val, c1[i].val, c2[i].val);
}
return c;
}
template <typename R>
vc<double> convolution_fft(const vc<R>& a, const vc<R>& b) {
using C = CFFT::C;
int need = (int)a.size() + (int)b.size() - 1;
int nbase = 1;
while ((1 << nbase) < need) nbase++;
CFFT::ensure_base(nbase);
int sz = 1 << nbase;
vector<C> fa(sz);
for (int i = 0; i < sz; i++) {
int x = (i < (int)a.size() ? a[i] : 0);
int y = (i < (int)b.size() ? b[i] : 0);
fa[i] = C(x, y);
}
CFFT::fft(fa, sz);
C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
for (int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
fa[i] = z;
}
for (int i = 0; i < (sz >> 1); i++) {
C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * CFFT::rts[(sz >> 1) + i];
fa[i] = A0 + A1 * s;
}
CFFT::fft(fa, sz >> 1);
vector<double> ret(need);
for (int i = 0; i < need; i++) {
ret[i] = (i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
}
return ret;
}
vector<ll> convolution(const vector<ll>& a, const vector<ll>& b) {
int n = len(a), m = len(b);
if (!n || !m) return {};
if (min(n, m) <= 2500) return convolution_naive(a, b);
ll abs_sum_a = 0, abs_sum_b = 0;
ll LIM = 1e15;
FOR(i, n) abs_sum_a = min(LIM, abs_sum_a + abs(a[i]));
FOR(i, m) abs_sum_b = min(LIM, abs_sum_b + abs(b[i]));
if (i128(abs_sum_a) * abs_sum_b < 1e15) {
vc<double> c = convolution_fft<ll>(a, b);
vc<ll> res(len(c));
FOR(i, len(c)) res[i] = ll(floor(c[i] + .5));
return res;
}
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static const unsigned long long i1 = mod_inv(MOD2 * MOD3, MOD1);
static const unsigned long long i2 = mod_inv(MOD1 * MOD3, MOD2);
static const unsigned long long i3 = mod_inv(MOD1 * MOD2, MOD3);
using mint1 = modint<MOD1>;
using mint2 = modint<MOD2>;
using mint3 = modint<MOD3>;
vc<mint1> a1(n), b1(m);
vc<mint2> a2(n), b2(m);
vc<mint3> a3(n), b3(m);
FOR(i, n) a1[i] = a[i], a2[i] = a[i], a3[i] = a[i];
FOR(i, m) b1[i] = b[i], b2[i] = b[i], b3[i] = b[i];
auto c1 = convolution_ntt<mint1>(a1, b1);
auto c2 = convolution_ntt<mint2>(a2, b2);
auto c3 = convolution_ntt<mint3>(a3, b3);
vc<ll> c(n + m - 1);
FOR(i, n + m - 1) {
u64 x = 0;
x += (c1[i].val * i1) % MOD1 * M2M3;
x += (c2[i].val * i2) % MOD2 * M1M3;
x += (c3[i].val * i3) % MOD3 * M1M2;
ll diff = c1[i].val - ((long long)(x) % (long long)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr unsigned long long offset[5]
= {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
template <typename mint>
vc<mint> convolution(const vc<mint>& a, const vc<mint>& b) {
int n = len(a), m = len(b);
if (!n || !m) return {};
if (mint::can_ntt()) {
if (min(n, m) <= 50) return convolution_karatsuba<mint>(a, b);
return convolution_ntt(a, b);
}
if (min(n, m) <= 200) return convolution_karatsuba<mint>(a, b);
return convolution_garner(a, b);
}
#line 2 "/home/maspy/compro/library/bigint/base.hpp"
// 10^9 ずつ区切って
struct BigInteger {
static constexpr int TEN[]
= {1, 10, 100, 1000, 10000,
100000, 1000000, 10000000, 100000000, 1000000000};
static constexpr int LOG = 9;
static constexpr int MOD = TEN[LOG];
using bint = BigInteger;
int sgn; // +1 or -1. 内部状態で -0 を許容する.
vc<int> dat;
BigInteger() : sgn(1) {}
BigInteger(i128 val) {
sgn = 1;
if (val != 0) {
if (val < 0) sgn = -1, val = -val;
while (val > 0) {
dat.eb(val % MOD);
val /= MOD;
}
}
}
BigInteger(string s) {
assert(!s.empty());
sgn = 1;
if (s[0] == '-') {
sgn = -1;
s.erase(s.begin());
assert(!s.empty());
}
if (s[0] == '0') s.clear();
reverse(all(s));
int n = len(s);
int m = ceil(n, LOG);
dat.assign(m, 0);
FOR(i, n) { dat[i / LOG] += TEN[i % LOG] * (s[i] - '0'); }
}
bint &operator=(const bint &p) {
sgn = p.sgn;
dat = p.dat;
return *this;
}
bool operator<(const bint &p) const {
if (sgn != p.sgn) return sgn < p.sgn;
if (len(dat) != len(p.dat)) {
if (sgn == 1) return len(dat) < len(p.dat);
if (sgn == -1) return len(dat) > len(p.dat);
}
FOR_R(i, len(dat)) {
if (dat[i] == p.dat[i]) continue;
if (sgn == 1) return dat[i] < p.dat[i];
if (sgn == -1) return dat[i] > p.dat[i];
}
return false;
}
bool operator>(const bint &p) const { return p < *this; }
bool operator<=(const bint &p) const { return !(*this > p); }
bool operator>=(const bint &p) const { return !(*this < p); }
bint &operator+=(const bint p) {
if (sgn != p.sgn) {
*this -= (-p);
return *this;
}
int n = max(len(dat), len(p.dat));
dat.resize(n + 1);
FOR(i, n) {
if (i < len(p.dat)) dat[i] += p.dat[i];
if (dat[i] >= MOD) dat[i] -= MOD, dat[i + 1] += 1;
}
while (len(dat) && dat.back() == 0) dat.pop_back();
return *this;
}
bint &operator-=(const bint p) {
if (sgn != p.sgn) {
*this += (-p);
return *this;
}
if ((sgn == 1 && *this < p) || (sgn == -1 && *this > p)) {
*this = p - *this;
sgn = -sgn;
return *this;
}
FOR(i, len(p.dat)) { dat[i] -= p.dat[i]; }
FOR(i, len(dat) - 1) {
if (dat[i] < 0) dat[i] += MOD, dat[i + 1] -= 1;
}
while (len(dat) && dat.back() == 0) { dat.pop_back(); }
return *this;
}
bint &operator*=(const bint &p) {
sgn *= p.sgn;
dat = convolve(dat, p.dat);
return *this;
}
// bint &operator/=(const bint &p) { return *this; }
bint operator-() const {
bint p = *this;
p.sgn *= -1;
return p;
}
bint operator+(const bint &p) const { return bint(*this) += p; }
bint operator-(const bint &p) const { return bint(*this) -= p; }
bint operator*(const bint &p) const { return bint(*this) *= p; }
// bint operator/(const modint &p) const { return modint(*this) /= p; }
bool operator==(const bint &p) const {
return (sgn == p.sgn && dat == p.dat);
}
bool operator!=(const bint &p) const {
return (sgn != p.sgn || dat != p.dat);
}
vc<int> convolve(const vc<int> &a, const vc<int> &b) {
int n = len(a), m = len(b);
if (!n || !m) return {};
if (min(n, m) <= 500) {
vc<int> c(n + m - 1);
u128 x = 0;
FOR(k, n + m - 1) {
int s = max<int>(0, k + 1 - m), t = min<int>(k, n - 1);
FOR(i, s, t + 1) { x += u64(a[i]) * b[k - i]; }
c[k] = x % MOD, x = x / MOD;
}
while (x > 0) { c.eb(x % MOD), x = x / MOD; }
return c;
}
static constexpr int p0 = 167772161;
static constexpr int p1 = 469762049;
static constexpr int p2 = 754974721;
using mint0 = modint<p0>;
using mint1 = modint<p1>;
using mint2 = modint<p2>;
vc<mint0> a0(all(a)), b0(all(b));
vc<mint1> a1(all(a)), b1(all(b));
vc<mint2> a2(all(a)), b2(all(b));
auto c0 = convolution_ntt<mint0>(a0, b0);
auto c1 = convolution_ntt<mint1>(a1, b1);
auto c2 = convolution_ntt<mint2>(a2, b2);
vc<int> c(len(c0));
u128 x = 0;
FOR(i, n + m - 1) {
x += CRT3<u128, p0, p1, p2>(c0[i].val, c1[i].val, c2[i].val);
c[i] = x % MOD, x = x / MOD;
}
while (x) { c.eb(x % MOD), x = x / MOD; }
return c;
}
string to_string() {
if (dat.empty()) return "0";
string s;
for (int x: dat) {
FOR(LOG) {
s += '0' + (x % 10);
x = x / 10;
}
}
while (s.back() == '0') s.pop_back();
if (sgn == -1) s += '-';
reverse(all(s));
return s;
}
// https://codeforces.com/contest/504/problem/D
string to_binary_string() {
vc<u32> A(all(dat));
string ANS;
while (1) {
while (len(A) && A.back() == u32(0)) POP(A);
if (A.empty()) break;
u64 rem = 0;
FOR_R(i, len(A)) {
rem = rem * MOD + A[i];
A[i] = rem >> 32;
rem &= u32(-1);
}
FOR(i, 32) { ANS += '0' + (rem >> i & 1); }
}
while (len(ANS) && ANS.back() == '0') ANS.pop_back();
reverse(all(ANS));
if (ANS.empty()) ANS += '0';
return ANS;
}
// https://codeforces.com/contest/759/problem/E
pair<bint, int> divmod(int p) {
vc<int> after;
ll rm = 0;
FOR_R(i, len(dat)) {
rm = rm * MOD + dat[i];
after.eb(rm / p);
rm = rm % p;
}
reverse(all(after));
while (len(after) && after.back() == 0) POP(after);
bint q;
q.sgn = sgn;
q.dat = after;
rm *= sgn;
if (rm < 0) {
rm += p;
q -= 1;
}
return {q, rm};
}
// https://codeforces.com/problemset/problem/582/D
vc<int> base_p_representation(int p) {
vc<u32> A(all(dat));
vc<int> res;
while (1) {
while (len(A) && A.back() == u32(0)) POP(A);
if (A.empty()) break;
u64 rm = 0;
FOR_R(i, len(A)) {
rm = rm * MOD + A[i];
A[i] = rm / p;
rm %= p;
}
res.eb(rm);
}
reverse(all(res));
return res;
}
// overflow 無視して計算
ll to_ll() {
ll x = 0;
FOR_R(i, len(dat)) x = MOD * x + dat[i];
return sgn * x;
}
// https://codeforces.com/contest/986/problem/D
bint pow(ll n) {
auto dfs = [&](auto &dfs, ll n) -> bint {
if (n == 1) return (*this);
bint x = dfs(dfs, n / 2);
x *= x;
if (n & 1) x *= (*this);
return x;
};
if (n == 0) return bint(1);
return dfs(dfs, n);
}
// https://codeforces.com/contest/986/problem/D
double log10() {
assert(!dat.empty() && sgn == 1);
if (len(dat) <= 3) {
double x = 0;
FOR_R(i, len(dat)) x = MOD * x + dat[i];
return std::log10(x);
}
double x = 0;
FOR(i, 4) x = MOD * x + dat[len(dat) - 1 - i];
x = std::log10(x);
x += double(LOG) * (len(dat) - 4);
return x;
}
};
#ifdef FASTIO
void wt(BigInteger x) { fastio::wt(x.to_string()); }
void rd(BigInteger &x) {
string s;
fastio::rd(s);
x = BigInteger(s);
}
#endif
#line 6 "main.cpp"
using B = BigInteger;
void solve() {
U64(N, D, M, S);
B b = 1;
FOR(S) b += b;
/*
差が 1 未満
|1/D - M/2^S|n < 1
|2^S-MD|n < 2^SD
*/
B r = b * B(D);
B l = b - B(M) * B(D);
if (l < 0) l = -l;
auto check = [&](ll n) -> bool { return l * B(n) < r; };
N = binary_search(check, 0, N + 1);
u64 X = floor_sum_of_linear<u128, u128>(0, N + 1, 1, 0, D);
u64 Y = floor_sum_of_linear<u128, u128>(0, N + 1, u128(M), 0, u128(1) << S);
if (Y - X > N) swap(X, Y);
u64 ANS = Y - X;
ANS = N - ANS;
print(ANS);
}
signed main() {
INT(T);
FOR(T) solve();
return 0;
}