結果
| 問題 | No.3478 XOR-Folding Primes |
| コンテスト | |
| ユーザー |
 NyaanNyaan
|
| 提出日時 | 2026-03-20 21:58:11 |
| 言語 | C++17 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
AC
|
| 実行時間 | 444 ms / 4,000 ms |
| コード長 | 22,200 bytes |
| 記録 | |
| コンパイル時間 | 3,427 ms |
| コンパイル使用メモリ | 317,096 KB |
| 実行使用メモリ | 10,236 KB |
| 最終ジャッジ日時 | 2026-03-20 21:58:23 |
| 合計ジャッジ時間 | 4,492 ms |
|
ジャッジサーバーID （参考情報） |
judge3_1 / judge2_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 8 |
ソースコード
/**
* date : 2026-03-20 21:58:06
* author : Nyaan
*/
#define NDEBUG
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <optional>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tr2/dynamic_bitset>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
constexpr P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(T &v) {
return next_permutation(begin(v), end(v));
}
// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
T res = I;
for (; n; f(a = a * a), n >>= 1) {
if (n & 1) f(res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
template <typename T>
T Rev(const T &v) {
T res = v;
reverse(begin(res), end(res));
return res;
}
template <typename T>
vector<T> Transpose(const vector<T> &v) {
using U = typename T::value_type;
if(v.empty()) return {};
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
res[j][i] = v[i][j];
}
}
return res;
}
template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
using U = typename T::value_type;
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
if (clockwise) {
res[W - 1 - j][i] = v[i][j];
} else {
res[j][H - 1 - i] = v[i][j];
}
}
}
return res;
}
} // namespace Nyaan
// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
// inout
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
// debug
#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif
// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
//
// Prime -> {0, 0, 1, 1, 0, 1, 0, 1, ...}
vector<bool> prime_sieve(int N) {
vector<bool> sieve(max(1, N) + 1, 1);
sieve[0] = sieve[1] = false;
for (int i = 2; i * i <= N; i++)
if (sieve[i] == true)
for (int j = i * i; j <= N; j += i) sieve[j] = false;
return sieve;
}
//
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
static_assert(r * mod == 1, "this code has bugs.");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint operator+() const { return mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const {
int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, u -= t * v;
tmp = x, x = y, y = tmp;
tmp = u, u = v, v = tmp;
}
return mint{u};
}
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
using namespace std;
// コンストラクタの MAX に 「C(n, r) や fac(n) でクエリを投げる最大の n 」
// を入れると倍速くらいになる
// mod を超えて前計算して 0 割りを踏むバグは対策済み
template <typename T>
struct Binomial {
vector<T> f, g, h;
Binomial(int MAX = 0) {
assert(T::get_mod() != 0 && "Binomial<mint>()");
f.resize(1, T{1});
g.resize(1, T{1});
h.resize(1, T{1});
if (MAX > 0) extend(MAX + 1);
}
void extend(int m = -1) {
int n = f.size();
if (m == -1) m = n * 2;
m = min<int>(m, T::get_mod());
if (n >= m) return;
f.resize(m);
g.resize(m);
h.resize(m);
for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);
g[m - 1] = f[m - 1].inverse();
h[m - 1] = g[m - 1] * f[m - 2];
for (int i = m - 2; i >= n; i--) {
g[i] = g[i + 1] * T(i + 1);
h[i] = g[i] * f[i - 1];
}
}
T fac(int i) {
if (i < 0) return T(0);
while (i >= (int)f.size()) extend();
return f[i];
}
T finv(int i) {
if (i < 0) return T(0);
while (i >= (int)g.size()) extend();
return g[i];
}
T inv(int i) {
if (i < 0) return -inv(-i);
while (i >= (int)h.size()) extend();
return h[i];
}
T C(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
return fac(n) * finv(n - r) * finv(r);
}
inline T operator()(int n, int r) { return C(n, r); }
template <typename I>
T multinomial(const vector<I>& r) {
static_assert(is_integral<I>::value == true);
int n = 0;
for (auto& x : r) {
if (x < 0) return T(0);
n += x;
}
T res = fac(n);
for (auto& x : r) res *= finv(x);
return res;
}
template <typename I>
T operator()(const vector<I>& r) {
return multinomial(r);
}
T C_naive(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
T ret = T(1);
r = min(r, n - r);
for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);
return ret;
}
T P(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
return fac(n) * finv(n - r);
}
// [x^r] 1 / (1-x)^n
T H(long long n, long long r) {
if (n < 0 || r < 0) return T(0);
return r == 0 ? 1 : C(n + r - 1, r);
}
};
//
using namespace std;
// {rank, det(非正方行列の場合は未定義)} を返す
// 型が double や Rational でも動くはず？(未検証)
//
// pivot 候補 : [0, pivot_end)
template <typename T>
std::pair<int, T> GaussElimination(vector<vector<T>> &a, int pivot_end = -1,
bool diagonalize = false) {
if (a.empty()) return {0, 1};
int H = a.size(), W = a[0].size(), rank = 0;
if (pivot_end == -1) pivot_end = W;
T det = 1;
for (int j = 0; j < pivot_end; j++) {
int idx = -1;
for (int i = rank; i < H; i++) {
if (a[i][j] != T(0)) {
idx = i;
break;
}
}
if (idx == -1) {
det = 0;
continue;
}
if (rank != idx) det = -det, swap(a[rank], a[idx]);
det *= a[rank][j];
if (diagonalize && a[rank][j] != T(1)) {
T coeff = T(1) / a[rank][j];
for (int k = j; k < W; k++) a[rank][k] *= coeff;
}
int is = diagonalize ? 0 : rank + 1;
for (int i = is; i < H; i++) {
if (i == rank) continue;
if (a[i][j] != T(0)) {
T coeff = a[i][j] / a[rank][j];
for (int k = j; k < W; k++) a[i][k] -= a[rank][k] * coeff;
}
}
rank++;
}
return make_pair(rank, det);
}
template <typename mint>
vector<vector<mint>> inverse_matrix(const vector<vector<mint>>& a) {
int N = a.size();
assert(N > 0);
assert(N == (int)a[0].size());
vector<vector<mint>> m(N, vector<mint>(2 * N));
for (int i = 0; i < N; i++) {
copy(begin(a[i]), end(a[i]), begin(m[i]));
m[i][N + i] = 1;
}
auto [rank, det] = GaussElimination(m, N, true);
if (rank != N) return {};
vector<vector<mint>> b(N);
for (int i = 0; i < N; i++) {
copy(begin(m[i]) + N, end(m[i]), back_inserter(b[i]));
}
return b;
}
template <class T>
struct Matrix {
vector<vector<T> > A;
Matrix() = default;
Matrix(int n, int m) : A(n, vector<T>(m, T())) {}
Matrix(int n) : A(n, vector<T>(n, T())){};
int H() const { return A.size(); }
int W() const { return A[0].size(); }
int size() const { return A.size(); }
inline const vector<T> &operator[](int k) const { return A[k]; }
inline vector<T> &operator[](int k) { return A[k]; }
static Matrix I(int n) {
Matrix mat(n);
for (int i = 0; i < n; i++) mat[i][i] = 1;
return (mat);
}
Matrix &operator+=(const Matrix &B) {
int n = H(), m = W();
assert(n == B.H() && m == B.W());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];
return (*this);
}
Matrix &operator-=(const Matrix &B) {
int n = H(), m = W();
assert(n == B.H() && m == B.W());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];
return (*this);
}
Matrix &operator*=(const Matrix &B) {
int n = H(), m = B.W(), p = W();
assert(p == B.H());
vector<vector<T> > C(n, vector<T>(m, T{}));
for (int i = 0; i < n; i++)
for (int k = 0; k < p; k++)
for (int j = 0; j < m; j++) C[i][j] += (*this)[i][k] * B[k][j];
A.swap(C);
return (*this);
}
Matrix &operator^=(long long k) {
Matrix B = Matrix::I(H());
while (k > 0) {
if (k & 1) B *= *this;
*this *= *this;
k >>= 1LL;
}
A.swap(B.A);
return (*this);
}
Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }
bool operator==(const Matrix &B) const {
assert(H() == B.H() && W() == B.W());
for (int i = 0; i < H(); i++)
for (int j = 0; j < W(); j++)
if (A[i][j] != B[i][j]) return false;
return true;
}
bool operator!=(const Matrix &B) const {
assert(H() == B.H() && W() == B.W());
for (int i = 0; i < H(); i++)
for (int j = 0; j < W(); j++)
if (A[i][j] != B[i][j]) return true;
return false;
}
Matrix inverse() const {
assert(H() == W());
Matrix B(H());
B.A = inverse_matrix(A);
return B;
}
friend ostream &operator<<(ostream &os, const Matrix &p) {
int n = p.H(), m = p.W();
for (int i = 0; i < n; i++) {
os << (i ? " " : "") << "[";
for (int j = 0; j < m; j++) {
os << p[i][j] << (j + 1 == m ? "]\n" : ",");
}
}
return (os);
}
T determinant() const {
Matrix B(*this);
assert(H() == W());
T ret = 1;
for (int i = 0; i < H(); i++) {
int idx = -1;
for (int j = i; j < W(); j++) {
if (B[j][i] != 0) {
idx = j;
break;
}
}
if (idx == -1) return 0;
if (i != idx) {
ret *= T(-1);
swap(B[i], B[idx]);
}
ret *= B[i][i];
T inv = T(1) / B[i][i];
for (int j = 0; j < W(); j++) {
B[i][j] *= inv;
}
for (int j = i + 1; j < H(); j++) {
T a = B[j][i];
if (a == 0) continue;
for (int k = i; k < W(); k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return ret;
}
};
/**
* @brief 行列ライブラリ
*/
//
using namespace Nyaan;
using mint = LazyMontgomeryModInt<998244353>;
// using mint = LazyMontgomeryModInt<1000000007>;
using vm = vector<mint>;
using vvm = vector<vm>;
Binomial<mint> C;
using namespace Nyaan;
void q() {
int MAX = TEN(7) + 1000;
auto sieve = prime_sieve(MAX);
vi ps, qs;
rep1(i, MAX) {
if (sieve[i]) ps.push_back(i);
if (sieve[i] and sieve[i ^ 2]) qs.push_back(i);
}
ini(T);
rep(t, T) {
ini(N, M);
if (N == 1) {
out(ub(ps, M));
} else {
int x = ub(qs, M);
rep(d, 100) {
int y = M - d;
if (y < 0) continue;
if (sieve[y] and sieve[y ^ 2] and (y ^ 2) > M) x--;
}
trc(x);
Matrix<mint> m(2);
m[0][0] = m[0][1] = 1;
m[1][0] = x;
m = m ^ (N - 1);
out(mint{x} * (m[0][0] + m[0][1]) + m[1][0] + m[1][1]);
}
}
}
void Nyaan::solve() {
int t = 1;
// in(t);
while (t--) q();
}