結果
| 問題 | No.2132 1 or X Game |
| ユーザー |
 kaichou243
|
| 提出日時 | 2022-11-25 22:22:22 |
| 言語 | C++17 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 65,043 bytes |
| コンパイル時間 | 3,477 ms |
| コンパイル使用メモリ | 317,712 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-04-10 03:33:00 |
| 合計ジャッジ時間 | 5,303 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
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
6,812 KB |
| testcase_01 | WA | - |
| testcase_02 | WA | - |
| testcase_03 | WA | - |
| testcase_04 | WA | - |
| testcase_05 | WA | - |
| testcase_06 | WA | - |
| testcase_07 | WA | - |
| testcase_08 | WA | - |
| testcase_09 | WA | - |
| testcase_10 | WA | - |
| testcase_11 | WA | - |
ソースコード
#include<bits/stdc++.h>
#include <immintrin.h>
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#define FOR(i,n) for(int i = 0; i < (n); i++)
#define sz(c) ((int)(c).size())
#define ten(x) ((int)1e##x)
#define all(v) (v).begin(), (v).end()
using namespace std;
using ll=long long;
using P = pair<ll,ll>;
const long double PI=acos(-1);
const ll INF=1e18;
const int inf=1e9;
struct Edge {
ll to;
ll cost;
};
using Graph=vector<vector<Edge>>;
template <typename T>
bool chmax(T &a,const T& b){
if (a<b){
a=b;
return true;
}
return false;
}
template <typename T>
bool chmin(T &a,const T& b){
if (a>b){
a=b;
return true;
}
return false;
}
template<int MOD> struct Fp{
ll val;
constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
if (val < 0) val += MOD;
}
static constexpr int getmod() { return MOD; }
constexpr Fp operator - () const noexcept {
return val ? MOD - val : 0;
}
constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
constexpr Fp& operator += (const Fp& r) noexcept {
val += r.val;
if (val >= MOD) val -= MOD;
return *this;
}
constexpr Fp& operator -= (const Fp& r) noexcept {
val -= r.val;
if (val < 0) val += MOD;
return *this;
}
constexpr Fp& operator *= (const Fp& r) noexcept {
val = val * r.val % MOD;
return *this;
}
constexpr Fp& operator /= (const Fp& r) noexcept {
ll a = r.val, b = MOD, u = 1, v = 0;
while (b) {
ll t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
val = val * u % MOD;
if (val < 0) val += MOD;
return *this;
}
constexpr bool operator == (const Fp& r) const noexcept {
return this->val == r.val;
}
constexpr bool operator != (const Fp& r) const noexcept {
return this->val != r.val;
}
constexpr bool operator < (const Fp& r) const noexcept {
return this->val < r.val;
}
friend constexpr istream& operator >> (istream& is, Fp<MOD>& x) noexcept {
is >> x.val;
x.val %= MOD;
if (x.val < 0) x.val += MOD;
return is;
}
friend constexpr ostream& operator << (ostream& os, const Fp<MOD>& x) noexcept {
return os << x.val;
}
friend constexpr Fp<MOD> modpow(const Fp<MOD>& a, long long n) noexcept {
Fp<MOD> res=1,r=a;
while(n){
if(n&1) res*=r;
r*=r;
n>>=1;
}
return res;
}
friend constexpr Fp<MOD> modinv(const Fp<MOD>& r) noexcept {
long long a = r.val, b = MOD, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
return Fp<MOD>(u);
}
ll get(){
return val;
}
explicit operator bool()const{
return val;
}
};
template< uint32_t mod, bool fast = false >
struct MontgomeryModInt {
using mint = MontgomeryModInt;
using i32 = int32_t;
using i64 = int64_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(r * mod == 1, "invalid, r * mod != 1");
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
u32 a;
MontgomeryModInt() : a{} {}
MontgomeryModInt(const i64 &x)
: a(reduce(u64(fast ? x : (x % mod + mod)) * n2)) {}
static constexpr u32 reduce(const u64 &b) {
return u32(b >> 32) + mod - u32((u64(u32(b) * r) * mod) >> 32);
}
constexpr mint& operator+=(const mint &p) {
if(i32(a += p.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint& operator-=(const mint &p) {
if(i32(a -= p.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint& operator*=(const mint &p) {
a = reduce(u64(a) * p.a);
return *this;
}
constexpr mint& operator/=(const mint &p) {
*this *= modinv(p);
return *this;
}
constexpr mint operator-() const { return mint() - *this; }
constexpr mint operator+(const mint &p) const { return mint(*this) += p; }
constexpr mint operator-(const mint &p) const { return mint(*this) -= p; }
constexpr mint operator*(const mint &p) const { return mint(*this) *= p; }
constexpr mint operator/(const mint &p) const { return mint(*this) /= p; }
constexpr bool operator==(const mint &p) const { return (a >= mod ? a - mod : a) == (p.a >= mod ? p.a - mod : p.a); }
constexpr bool operator!=(const mint &p) const { return (a >= mod ? a - mod : a) != (p.a >= mod ? p.a - mod : p.a); }
u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
friend constexpr MontgomeryModInt<mod> modpow(const MontgomeryModInt<mod> &x,u64 n) noexcept {
MontgomeryModInt<mod> ret(1), mul(x);
while(n > 0) {
if(n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend constexpr MontgomeryModInt<mod> modinv(const MontgomeryModInt<mod> &r) noexcept {
u64 a = r.get(), b = mod, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
return MontgomeryModInt<mod>(u);
}
friend ostream &operator<<(ostream &os, const mint &p) {
return os << p.get();
}
friend istream &operator>>(istream &is, mint &a) {
i64 t;
is >> t;
a = mint(t);
return is;
}
static constexpr u32 getmod() { return mod; }
};
template<class T,T (*op)(T,T),T (*e)()> struct SegmentTree{
int n;
vector<T> dat;
SegmentTree(int N){
n=1;
while(n<N)n*=2;
dat.assign(2*n,e());
}
void add(int k,T x){
k+=n;
dat[k]+=x;
while(k){
k>>=1;
dat[k]=op(dat[k*2],dat[k*2+1]);
}
}
void apply(int k,T x){
k+=n;
dat[k]=op(dat[k],x);
while(k){
k>>=1;
dat[k]=op(dat[k*2],dat[k*2+1]);
}
}
void set(int k,T x){
k+=n;
dat[k]=x;
while(k){
k>>=1;
dat[k]=op(dat[k*2],dat[k*2+1]);
}
}
T query(int l,int r){
T prodl=e(),prodr=e();
l+=n;
r+=n;
while(l<r){
if(l&1) prodl=op(prodl,dat[l++]);
if(r&1) prodr=op(dat[--r],prodr);
l>>=1;
r>>=1;
}
return op(prodl,prodr);
}
};
struct FenwickTree{
int n;
vector<ll> dat;
FenwickTree(int N){
n=1;
while(n<N) n*=2;
dat.assign(n,0);
}
void add(int k,ll x){
k+=1;
while(k<=n){
dat[k]+=x;
k+=k&-k;
}
}
//sum[0,k)
ll sum(int k){
ll ans=0;
while(k){
ans+=dat[k];
k-=k&-k;
}
return ans;
}
//sum[l,r)
ll sum(int l,int r){
return sum(r)-sum(l);
}
};
template<class S,S (*op)(S,S),S (*e)(),class F,S (*mapping)(F,S),F (*composition)(F,F),F (*id)()>
struct LazySegTree{
private:
int _n,size=1,idx=0;
vector<S>seq;
vector<F>lazy;
void update(int k){seq[k]=op(seq[2*k],seq[2*k+1]);}
void all_apply(int k,F f){
seq[k]=mapping(f,seq[k]);
if(k<size)lazy[k]=composition(f,lazy[k]);
}
void eval(int k){
all_apply(2*k,lazy[k]);
all_apply(2*k+1,lazy[k]);
lazy[k]=id();
}
public:
LazySegTree(int n):LazySegTree(vector<S>(n,e())){}
LazySegTree(const vector<S>&v):_n(int(v.size())){
while(size<_n)size<<=1,idx++;
seq=vector<S>(2*size,e());
lazy=vector<F>(2*size,id());
for(int i=0;i<_n;i++)seq[size+i]=v[i];
for(int i=size-1;i>=1;i--)update(i);
}
void set(int p,S x){
p+=size;
for(int i=idx;i>=1;i--)eval(p>>i);
seq[p]=x;
for(int i=1;i<=idx;i++)update(p>>i);
}
void add(int p,ll x){
p+=size;
for(int i=idx;i>=1;i--)eval(p>>i);
seq[p].value+=x;
for(int i=1;i<=idx;i++)update(p>>i);
}
S operator[](int p){
p+=size;
for(int i=idx;i>=1;i--)eval(p>>i);
return seq[p];
}
S query(int l,int r){
if(l==r)return e();
S sml=e(),smr=e();
l+=size,r+=size;
for(int i=idx;i>=1;i--){
if(((l>>i)<<i)!=l)eval(l>>i);
if(((r>>i)<<i)!=r)eval(r>>i);
}
while(l<r){
if(l&1)sml=op(sml,seq[l++]);
if(r&1)smr=op(seq[--r],smr);
l>>=1,r>>=1;
}
return op(sml,smr);
}
S all_query()const{return seq[1];}
void apply(int p,F f){
p+=size;
for(int i=idx;i>=1;i--)eval(p>>i);
seq[p]=mapping(f,seq[p]);
for(int i=1;i<=idx;i++)update(p>>i);
}
void apply(int l,int r,F f){
if(l==r)return ;
l+=size;
r+=size;
for(int i=idx;i>=1;i--){
if(((l>>i)<<i)!=l)eval(l>>i);
if(((r>>i)<<i)!=r)eval((r-1)>>i);
}
int l2=l,r2=r;
while(l<r){
if(l&1)all_apply(l++,f);
if(r&1)all_apply(--r,f);
l>>=1;
r>>=1;
}
l=l2,r=r2;
for(int i=1;i<=idx;i++){
if(((l>>i)<<i)!=l)update(l>>i);
if(((r>>i)<<i)!=r)update((r-1)>>i);
}
}
};
ll mod(ll a,ll MOD){
if(a<0) a+=MOD;
return a%MOD;
}
ll modpow(ll a,ll n,ll mod){
ll res=1;
a%=mod;
while (n>0){
if (n & 1) res*=a;
a *= a;
a%=mod;
n >>= 1;
res%=mod;
}
return res;
}
vector<P> prime_factorize(ll N) {
vector<P> res;
for (ll a = 2; a * a <= N; ++a) {
if (N % a != 0) continue;
ll ex = 0;
while(N % a == 0){
++ex;
N /= a;
}
res.push_back({a, ex});
}
if (N != 1) res.push_back({N, 1});
return res;
}
ll modinv(ll a, ll mod) {
ll b = mod, u = 1, v = 0;
while (b) {
ll t = a/b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
u %= mod;
if (u < 0) u += mod;
return u;
}
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;
}
P ChineseRem(const vector<ll> &b, const vector<ll> &m) {
ll r = 0, M = 1;
for (int i = 0; i < (int)b.size(); ++i) {
ll p, q;
ll d = extGcd(M, m[i], p, q);
if ((b[i] - r) % d != 0) return make_pair(0, -1);
ll tmp = (b[i] - r) / d * p % (m[i]/d);
r += M * tmp;
M *= m[i]/d;
}
return make_pair(mod(r, M), M);
}
namespace NTT {
using i64 = int64_t;
__attribute__((target("sse4.2"))) inline __m128i my128_mullo_epu32(
const __m128i &a, const __m128i &b) {
return _mm_mullo_epi32(a, b);
}
__attribute__((target("sse4.2"))) inline __m128i my128_mulhi_epu32(
const __m128i &a, const __m128i &b) {
__m128i a13 = _mm_shuffle_epi32(a, 0xF5);
__m128i b13 = _mm_shuffle_epi32(b, 0xF5);
__m128i prod02 = _mm_mul_epu32(a, b);
__m128i prod13 = _mm_mul_epu32(a13, b13);
__m128i prod = _mm_unpackhi_epi64(_mm_unpacklo_epi32(prod02, prod13),
_mm_unpackhi_epi32(prod02, prod13));
return prod;
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_mul_128(
const __m128i &a, const __m128i &b, const __m128i &r, const __m128i &m1) {
return _mm_sub_epi32(
_mm_add_epi32(my128_mulhi_epu32(a, b), m1),
my128_mulhi_epu32(my128_mullo_epu32(my128_mullo_epu32(a, b), r), m1));
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_add_128(
const __m128i &a, const __m128i &b, const __m128i &m2, const __m128i &m0) {
__m128i ret = _mm_sub_epi32(_mm_add_epi32(a, b), m2);
return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_sub_128(
const __m128i &a, const __m128i &b, const __m128i &m2, const __m128i &m0) {
__m128i ret = _mm_sub_epi32(a, b);
return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}
__attribute__((target("avx2"))) inline __m256i my256_mullo_epu32(
const __m256i &a, const __m256i &b) {
return _mm256_mullo_epi32(a, b);
}
__attribute__((target("avx2"))) inline __m256i my256_mulhi_epu32(
const __m256i &a, const __m256i &b) {
__m256i a13 = _mm256_shuffle_epi32(a, 0xF5);
__m256i b13 = _mm256_shuffle_epi32(b, 0xF5);
__m256i prod02 = _mm256_mul_epu32(a, b);
__m256i prod13 = _mm256_mul_epu32(a13, b13);
__m256i prod = _mm256_unpackhi_epi64(_mm256_unpacklo_epi32(prod02, prod13),
_mm256_unpackhi_epi32(prod02, prod13));
return prod;
}
__attribute__((target("avx2"))) inline __m256i montgomery_mul_256(
const __m256i &a, const __m256i &b, const __m256i &r, const __m256i &m1) {
return _mm256_sub_epi32(
_mm256_add_epi32(my256_mulhi_epu32(a, b), m1),
my256_mulhi_epu32(my256_mullo_epu32(my256_mullo_epu32(a, b), r), m1));
}
__attribute__((target("avx2"))) inline __m256i montgomery_add_256(
const __m256i &a, const __m256i &b, const __m256i &m2, const __m256i &m0) {
__m256i ret = _mm256_sub_epi32(_mm256_add_epi32(a, b), m2);
return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
ret);
}
__attribute__((target("avx2"))) inline __m256i montgomery_sub_256(
const __m256i &a, const __m256i &b, const __m256i &m2, const __m256i &m0) {
__m256i ret = _mm256_sub_epi32(a, b);
return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
ret);
}
int calc_primitive_root(int mod) {
if (mod == 2) return 1;
if (mod == 167772161) return 3;
if (mod == 469762049) return 3;
if (mod == 754974721) return 11;
if (mod == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
long long x = (mod - 1) / 2;
while (x % 2 == 0) x /= 2;
for (long long i = 3; i * i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) x /= i;
}
}
if (x > 1) divs[cnt++] = x;
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (modpow(g, (mod - 1) / divs[i], mod) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
int get_fft_size(int N, int M) {
int size_a = 1, size_b = 1;
while (size_a < N) size_a <<= 1;
while (size_b < M) size_b <<= 1;
return max(size_a, size_b) << 1;
}
constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
template <class mint>
struct fft_info{
static constexpr int rank2 = bsf_constexpr(mint::getmod() - 1);
std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1
std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1
std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;
std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;
int g;
fft_info(){
int MOD=mint::getmod();
g=calc_primitive_root(MOD);
root[rank2] = modpow(mint(g),(MOD - 1) >> rank2);
iroot[rank2] = modinv(root[rank2]);
for (int i = rank2 - 1; i >= 0; i--) {
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];
}
}
{
mint 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 ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// number-theoretic transform
template <class mint>
void trans(std::vector<mint>& a) {
int n = int(a.size());
int h = ceil_pow2(n);
int MOD=a[0].getmod();
static const fft_info<mint> info;
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);
mint 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 *= info.rate2[bsf(~(unsigned int)(s))];
}
len++;
} else {
// 4-base
int p = 1 << (h - len - 2);
mint rot = 1, imag = info.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++) {
auto mod2 = 1ULL * MOD * MOD;
auto a0 = 1ULL * a[i + offset].get();
auto a1 = 1ULL * a[i + offset + p].get() * rot.get();
auto a2 = 1ULL * a[i + offset + 2 * p].get() * rot2.get();
auto a3 = 1ULL * a[i + offset + 3 * p].get() * rot3.get();
auto a1na3imag =
1ULL * mint(a1 + mod2 - a3).get() * imag.get();
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 *= info.rate3[bsf(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <class mint>
void trans_inv(std::vector<mint>& a) {
int n = int(a.size());
int h = ceil_pow2(n);
static const fft_info<mint> info;
int MOD=a[0].getmod();
int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint 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)(MOD + l.get() - r.get()) *
irot.get();
;
}
if (s + 1 != (1 << (len - 1)))
irot *= info.irate2[bsf(~(unsigned int)(s))];
}
len--;
} else {
// 4-base
int p = 1 << (h - len);
mint irot = 1, iimag = info.iroot[2];
for (int s = 0; s < (1 << (len - 2)); s++) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
auto a0 = 1ULL * a[i + offset + 0 * p].get();
auto a1 = 1ULL * a[i + offset + 1 * p].get();
auto a2 = 1ULL * a[i + offset + 2 * p].get();
auto a3 = 1ULL * a[i + offset + 3 * p].get();
auto a2na3iimag =
1ULL *
mint((MOD + a2 - a3) * iimag.get()).get();
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] =
(a0 + (MOD - a1) + a2na3iimag) * irot.get();
a[i + offset + 2 * p] =
(a0 + a1 + (MOD - a2) + (MOD - a3)) *
irot2.get();
a[i + offset + 3 * p] =
(a0 + (MOD - a1) + (MOD - a2na3iimag)) *
irot3.get();
}
if (s + 1 != (1 << (len - 2)))
irot *= info.irate3[bsf(~(unsigned int)(s))];
}
len -= 2;
}
}
}
namespace ntt_inner {
using u64 = uint64_t;
constexpr uint32_t get_pr(uint32_t mod) {
if (mod == 2) return 1;
u64 ds[32] = {};
int idx = 0;
u64 m = mod - 1;
for (u64 i = 2; i * i <= m; ++i) {
if (m % i == 0) {
ds[idx++] = i;
while (m % i == 0) m /= i;
}
}
if (m != 1) ds[idx++] = m;
uint32_t pr = 2;
while (1) {
int flg = 1;
for (int i = 0; i < idx; ++i) {
u64 a = pr, b = (mod - 1) / ds[i], r = 1;
while (b) {
if (b & 1) r = r * a % mod;
a = a * a % mod;
b >>= 1;
}
if (r == 1) {
flg = 0;
break;
}
}
if (flg == 1) break;
++pr;
}
return pr;
}
constexpr int SZ_FFT_BUF = 1 << 23;
uint32_t _buf1[SZ_FFT_BUF] __attribute__((aligned(64)));
uint32_t _buf2[SZ_FFT_BUF] __attribute__((aligned(64)));
} // namespace ntt_inner
template <typename mint>
struct NumberTheoreticTransform {
static constexpr uint32_t mod = mint::getmod();
static constexpr uint32_t pr = ntt_inner::get_pr(mint::getmod());
static constexpr int level = __builtin_ctzll(mod - 1);
mint dw[level], dy[level];
mint *buf1, *buf2;
constexpr NumberTheoreticTransform() {
setwy(level);
union raw_cast {
mint dat;
uint32_t _;
};
buf1 = &(((raw_cast *)(ntt_inner::_buf1))->dat);
buf2 = &(((raw_cast *)(ntt_inner::_buf2))->dat);
}
constexpr void setwy(int k) {
mint w[level], y[level];
w[k - 1] = modpow(mint(pr),(mod - 1) / (1 << k));
y[k - 1] = modinv(w[k - 1]);
for (int i = k - 2; i > 0; --i)
w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
dw[0] = dy[0] = w[1] * w[1];
dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
for (int i = 3; i < k; ++i) {
dw[i] = dw[i - 1] * y[i - 2] * w[i];
dy[i] = dy[i - 1] * w[i - 2] * y[i];
}
}
__attribute__((target("avx2"))) void ntt(mint *a, int n) {
int k = n ? __builtin_ctz(n) : 0;
if (k == 0) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
if (k & 1) {
int v = 1 << (k - 1);
if (v < 8) {
for (int j = 0; j < v; ++j) {
mint ajv = a[j + v];
a[j + v] = a[j] - ajv;
a[j] += ajv;
}
} else {
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m2 = _mm256_set1_epi32(mod + mod);
int j0 = 0;
int j1 = v;
for (; j0 < v; j0 += 8, j1 += 8) {
__m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
__m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
__m256i naj = montgomery_add_256(T0, T1, m2, m0);
__m256i najv = montgomery_sub_256(T0, T1, m2, m0);
_mm256_storeu_si256((__m256i *)(a + j0), naj);
_mm256_storeu_si256((__m256i *)(a + j1), najv);
}
}
}
int u = 1 << (2 + (k & 1));
int v = 1 << (k - 2 - (k & 1));
mint one = mint(1);
mint imag = dw[1];
while (v) {
if (v == 1) {
mint ww = one, xx = one, wx = one;
for (int jh = 0; jh < u;) {
ww = xx * xx, wx = ww * xx;
mint t0 = a[jh + 0], t1 = a[jh + 1] * xx;
mint t2 = a[jh + 2] * ww, t3 = a[jh + 3] * wx;
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[jh + 0] = t0p2 + t1p3, a[jh + 1] = t0p2 - t1p3;
a[jh + 2] = t0m2 + t1m3, a[jh + 3] = t0m2 - t1m3;
xx *= dw[__builtin_ctz((jh += 4))];
}
} else if (v == 4) {
const __m128i m0 = _mm_set1_epi32(0);
const __m128i m1 = _mm_set1_epi32(mod);
const __m128i m2 = _mm_set1_epi32(mod + mod);
const __m128i r = _mm_set1_epi32(mint::r);
const __m128i Imag = _mm_set1_epi32(imag.a);
mint ww = one, xx = one, wx = one;
for (int jh = 0; jh < u;) {
if (jh == 0) {
int j0 = 0;
int j1 = v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = v;
for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
const __m128i T0P2 = montgomery_add_128(T0, T2, m2, m0);
const __m128i T1P3 = montgomery_add_128(T1, T3, m2, m0);
const __m128i T0M2 = montgomery_sub_128(T0, T2, m2, m0);
const __m128i T1M3 = montgomery_mul_128(
montgomery_sub_128(T1, T3, m2, m0), Imag, r, m1);
_mm_storeu_si128((__m128i *)(a + j0),
montgomery_add_128(T0P2, T1P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j1),
montgomery_sub_128(T0P2, T1P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j2),
montgomery_add_128(T0M2, T1M3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j3),
montgomery_sub_128(T0M2, T1M3, m2, m0));
}
} else {
ww = xx * xx, wx = ww * xx;
const __m128i WW = _mm_set1_epi32(ww.a);
const __m128i WX = _mm_set1_epi32(wx.a);
const __m128i XX = _mm_set1_epi32(xx.a);
int j0 = jh * v;
int j1 = j0 + v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = j1;
for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
const __m128i MT1 = montgomery_mul_128(T1, XX, r, m1);
const __m128i MT2 = montgomery_mul_128(T2, WW, r, m1);
const __m128i MT3 = montgomery_mul_128(T3, WX, r, m1);
const __m128i T0P2 = montgomery_add_128(T0, MT2, m2, m0);
const __m128i T1P3 = montgomery_add_128(MT1, MT3, m2, m0);
const __m128i T0M2 = montgomery_sub_128(T0, MT2, m2, m0);
const __m128i T1M3 = montgomery_mul_128(
montgomery_sub_128(MT1, MT3, m2, m0), Imag, r, m1);
_mm_storeu_si128((__m128i *)(a + j0),
montgomery_add_128(T0P2, T1P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j1),
montgomery_sub_128(T0P2, T1P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j2),
montgomery_add_128(T0M2, T1M3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j3),
montgomery_sub_128(T0M2, T1M3, m2, m0));
}
}
xx *= dw[__builtin_ctz((jh += 4))];
}
} else {
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m1 = _mm256_set1_epi32(mod);
const __m256i m2 = _mm256_set1_epi32(mod + mod);
const __m256i r = _mm256_set1_epi32(mint::r);
const __m256i Imag = _mm256_set1_epi32(imag.a);
mint ww = one, xx = one, wx = one;
for (int jh = 0; jh < u;) {
if (jh == 0) {
int j0 = 0;
int j1 = v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = v;
for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
const __m256i T0P2 = montgomery_add_256(T0, T2, m2, m0);
const __m256i T1P3 = montgomery_add_256(T1, T3, m2, m0);
const __m256i T0M2 = montgomery_sub_256(T0, T2, m2, m0);
const __m256i T1M3 = montgomery_mul_256(
montgomery_sub_256(T1, T3, m2, m0), Imag, r, m1);
_mm256_storeu_si256((__m256i *)(a + j0),
montgomery_add_256(T0P2, T1P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j1),
montgomery_sub_256(T0P2, T1P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j2),
montgomery_add_256(T0M2, T1M3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j3),
montgomery_sub_256(T0M2, T1M3, m2, m0));
}
} else {
ww = xx * xx, wx = ww * xx;
const __m256i WW = _mm256_set1_epi32(ww.a);
const __m256i WX = _mm256_set1_epi32(wx.a);
const __m256i XX = _mm256_set1_epi32(xx.a);
int j0 = jh * v;
int j1 = j0 + v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = j1;
for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
const __m256i MT1 = montgomery_mul_256(T1, XX, r, m1);
const __m256i MT2 = montgomery_mul_256(T2, WW, r, m1);
const __m256i MT3 = montgomery_mul_256(T3, WX, r, m1);
const __m256i T0P2 = montgomery_add_256(T0, MT2, m2, m0);
const __m256i T1P3 = montgomery_add_256(MT1, MT3, m2, m0);
const __m256i T0M2 = montgomery_sub_256(T0, MT2, m2, m0);
const __m256i T1M3 = montgomery_mul_256(
montgomery_sub_256(MT1, MT3, m2, m0), Imag, r, m1);
_mm256_storeu_si256((__m256i *)(a + j0),
montgomery_add_256(T0P2, T1P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j1),
montgomery_sub_256(T0P2, T1P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j2),
montgomery_add_256(T0M2, T1M3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j3),
montgomery_sub_256(T0M2, T1M3, m2, m0));
}
}
xx *= dw[__builtin_ctz((jh += 4))];
}
}
u <<= 2;
v >>= 2;
}
}
__attribute__((target("avx2"))) void intt(mint *a, int n,
int normalize = true) {
int k = n ? __builtin_ctz(n) : 0;
if (k == 0) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
if (normalize) {
a[0] *= modinv(mint(2));
a[1] *= modinv(mint(2));
}
return;
}
int u = 1 << (k - 2);
int v = 1;
mint one = mint(1);
mint imag = dy[1];
while (u) {
if (v == 1) {
mint ww = one, xx = one, yy = one;
u <<= 2;
for (int jh = 0; jh < u;) {
ww = xx * xx, yy = xx * imag;
mint t0 = a[jh + 0], t1 = a[jh + 1];
mint t2 = a[jh + 2], t3 = a[jh + 3];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
a[jh + 0] = t0p1 + t2p3, a[jh + 2] = (t0p1 - t2p3) * ww;
a[jh + 1] = t0m1 + t2m3, a[jh + 3] = (t0m1 - t2m3) * ww;
xx *= dy[__builtin_ctz(jh += 4)];
}
} else if (v == 4) {
const __m128i m0 = _mm_set1_epi32(0);
const __m128i m1 = _mm_set1_epi32(mod);
const __m128i m2 = _mm_set1_epi32(mod + mod);
const __m128i r = _mm_set1_epi32(mint::r);
const __m128i Imag = _mm_set1_epi32(imag.a);
mint ww = one, xx = one, yy = one;
u <<= 2;
for (int jh = 0; jh < u;) {
if (jh == 0) {
int j0 = 0;
int j1 = v;
int j2 = v + v;
int j3 = j2 + v;
for (; j0 < v; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
const __m128i T0P1 = montgomery_add_128(T0, T1, m2, m0);
const __m128i T2P3 = montgomery_add_128(T2, T3, m2, m0);
const __m128i T0M1 = montgomery_sub_128(T0, T1, m2, m0);
const __m128i T2M3 = montgomery_mul_128(
montgomery_sub_128(T2, T3, m2, m0), Imag, r, m1);
_mm_storeu_si128((__m128i *)(a + j0),
montgomery_add_128(T0P1, T2P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j2),
montgomery_sub_128(T0P1, T2P3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j1),
montgomery_add_128(T0M1, T2M3, m2, m0));
_mm_storeu_si128((__m128i *)(a + j3),
montgomery_sub_128(T0M1, T2M3, m2, m0));
}
} else {
ww = xx * xx, yy = xx * imag;
const __m128i WW = _mm_set1_epi32(ww.a);
const __m128i XX = _mm_set1_epi32(xx.a);
const __m128i YY = _mm_set1_epi32(yy.a);
int j0 = jh * v;
int j1 = j0 + v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = j1;
for (; j0 < je; j0 += 4, j1 += 4, j2 += 4, j3 += 4) {
const __m128i T0 = _mm_loadu_si128((__m128i *)(a + j0));
const __m128i T1 = _mm_loadu_si128((__m128i *)(a + j1));
const __m128i T2 = _mm_loadu_si128((__m128i *)(a + j2));
const __m128i T3 = _mm_loadu_si128((__m128i *)(a + j3));
const __m128i T0P1 = montgomery_add_128(T0, T1, m2, m0);
const __m128i T2P3 = montgomery_add_128(T2, T3, m2, m0);
const __m128i T0M1 = montgomery_mul_128(
montgomery_sub_128(T0, T1, m2, m0), XX, r, m1);
__m128i T2M3 = montgomery_mul_128(
montgomery_sub_128(T2, T3, m2, m0), YY, r, m1);
_mm_storeu_si128((__m128i *)(a + j0),
montgomery_add_128(T0P1, T2P3, m2, m0));
_mm_storeu_si128(
(__m128i *)(a + j2),
montgomery_mul_128(montgomery_sub_128(T0P1, T2P3, m2, m0), WW,
r, m1));
_mm_storeu_si128((__m128i *)(a + j1),
montgomery_add_128(T0M1, T2M3, m2, m0));
_mm_storeu_si128(
(__m128i *)(a + j3),
montgomery_mul_128(montgomery_sub_128(T0M1, T2M3, m2, m0), WW,
r, m1));
}
}
xx *= dy[__builtin_ctz(jh += 4)];
}
} else {
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m1 = _mm256_set1_epi32(mod);
const __m256i m2 = _mm256_set1_epi32(mod + mod);
const __m256i r = _mm256_set1_epi32(mint::r);
const __m256i Imag = _mm256_set1_epi32(imag.a);
mint ww = one, xx = one, yy = one;
u <<= 2;
for (int jh = 0; jh < u;) {
if (jh == 0) {
int j0 = 0;
int j1 = v;
int j2 = v + v;
int j3 = j2 + v;
for (; j0 < v; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
const __m256i T0P1 = montgomery_add_256(T0, T1, m2, m0);
const __m256i T2P3 = montgomery_add_256(T2, T3, m2, m0);
const __m256i T0M1 = montgomery_sub_256(T0, T1, m2, m0);
const __m256i T2M3 = montgomery_mul_256(
montgomery_sub_256(T2, T3, m2, m0), Imag, r, m1);
_mm256_storeu_si256((__m256i *)(a + j0),
montgomery_add_256(T0P1, T2P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j2),
montgomery_sub_256(T0P1, T2P3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j1),
montgomery_add_256(T0M1, T2M3, m2, m0));
_mm256_storeu_si256((__m256i *)(a + j3),
montgomery_sub_256(T0M1, T2M3, m2, m0));
}
} else {
ww = xx * xx, yy = xx * imag;
const __m256i WW = _mm256_set1_epi32(ww.a);
const __m256i XX = _mm256_set1_epi32(xx.a);
const __m256i YY = _mm256_set1_epi32(yy.a);
int j0 = jh * v;
int j1 = j0 + v;
int j2 = j1 + v;
int j3 = j2 + v;
int je = j1;
for (; j0 < je; j0 += 8, j1 += 8, j2 += 8, j3 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
const __m256i T2 = _mm256_loadu_si256((__m256i *)(a + j2));
const __m256i T3 = _mm256_loadu_si256((__m256i *)(a + j3));
const __m256i T0P1 = montgomery_add_256(T0, T1, m2, m0);
const __m256i T2P3 = montgomery_add_256(T2, T3, m2, m0);
const __m256i T0M1 = montgomery_mul_256(
montgomery_sub_256(T0, T1, m2, m0), XX, r, m1);
const __m256i T2M3 = montgomery_mul_256(
montgomery_sub_256(T2, T3, m2, m0), YY, r, m1);
_mm256_storeu_si256((__m256i *)(a + j0),
montgomery_add_256(T0P1, T2P3, m2, m0));
_mm256_storeu_si256(
(__m256i *)(a + j2),
montgomery_mul_256(montgomery_sub_256(T0P1, T2P3, m2, m0), WW,
r, m1));
_mm256_storeu_si256((__m256i *)(a + j1),
montgomery_add_256(T0M1, T2M3, m2, m0));
_mm256_storeu_si256(
(__m256i *)(a + j3),
montgomery_mul_256(montgomery_sub_256(T0M1, T2M3, m2, m0), WW,
r, m1));
}
}
xx *= dy[__builtin_ctz(jh += 4)];
}
}
u >>= 4;
v <<= 2;
}
if (k & 1) {
v = 1 << (k - 1);
if (v < 8) {
for (int j = 0; j < v; ++j) {
mint ajv = a[j] - a[j + v];
a[j] += a[j + v];
a[j + v] = ajv;
}
} else {
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m2 = _mm256_set1_epi32(mod + mod);
int j0 = 0;
int j1 = v;
for (; j0 < v; j0 += 8, j1 += 8) {
const __m256i T0 = _mm256_loadu_si256((__m256i *)(a + j0));
const __m256i T1 = _mm256_loadu_si256((__m256i *)(a + j1));
__m256i naj = montgomery_add_256(T0, T1, m2, m0);
__m256i najv = montgomery_sub_256(T0, T1, m2, m0);
_mm256_storeu_si256((__m256i *)(a + j0), naj);
_mm256_storeu_si256((__m256i *)(a + j1), najv);
}
}
}
if (normalize) {
mint invn = modinv(mint(n));
for (int i = 0; i < n; i++) a[i] *= invn;
}
}
__attribute__((target("avx2"))) void inplace_multiply(
int l1, int l2, int zero_padding = true) {
int l = l1 + l2 - 1;
int M = 4;
while (M < l) M <<= 1;
if (zero_padding) {
for (int i = l1; i < M; i++) ntt_inner::_buf1[i] = 0;
for (int i = l2; i < M; i++) ntt_inner::_buf2[i] = 0;
}
const __m256i m0 = _mm256_set1_epi32(0);
const __m256i m1 = _mm256_set1_epi32(mod);
const __m256i r = _mm256_set1_epi32(mint::r);
const __m256i N2 = _mm256_set1_epi32(mint::n2);
for (int i = 0; i < l1; i += 8) {
__m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i));
__m256i b = montgomery_mul_256(a, N2, r, m1);
_mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), b);
}
for (int i = 0; i < l2; i += 8) {
__m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf2 + i));
__m256i b = montgomery_mul_256(a, N2, r, m1);
_mm256_storeu_si256((__m256i *)(ntt_inner::_buf2 + i), b);
}
ntt(buf1, M);
ntt(buf2, M);
for (int i = 0; i < M; i += 8) {
__m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i));
__m256i b = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf2 + i));
__m256i c = montgomery_mul_256(a, b, r, m1);
_mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), c);
}
intt(buf1, M, false);
const __m256i INVM = _mm256_set1_epi32((mint(M).inverse()).a);
for (int i = 0; i < l; i += 8) {
__m256i a = _mm256_loadu_si256((__m256i *)(ntt_inner::_buf1 + i));
__m256i b = montgomery_mul_256(a, INVM, r, m1);
__m256i c = my256_mulhi_epu32(my256_mullo_epu32(b, r), m1);
__m256i d = _mm256_and_si256(_mm256_cmpgt_epi32(c, m0), m1);
__m256i e = _mm256_sub_epi32(d, c);
_mm256_storeu_si256((__m256i *)(ntt_inner::_buf1 + i), e);
}
}
void ntt(vector<mint> &a) {
int M = (int)a.size();
for (int i = 0; i < M; i++) buf1[i].a = a[i].a;
ntt(buf1, M);
for (int i = 0; i < M; i++) a[i].a = buf1[i].a;
}
void intt(vector<mint> &a) {
int M = (int)a.size();
for (int i = 0; i < M; i++) buf1[i].a = a[i].a;
intt(buf1, M, true);
for (int i = 0; i < M; i++) a[i].a = buf1[i].a;
}
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
if (a.size() == 0 && b.size() == 0) return vector<mint>{};
int l = a.size() + b.size() - 1;
if (min<int>(a.size(), b.size()) <= 40) {
vector<mint> s(l);
for (int i = 0; i < (int)a.size(); ++i)
for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
return s;
}
assert(l <= ntt_inner::SZ_FFT_BUF);
int M = 4;
while (M < l) M <<= 1;
for (int i = 0; i < (int)a.size(); ++i) buf1[i].a = a[i].a;
for (int i = (int)a.size(); i < M; ++i) buf1[i].a = 0;
for (int i = 0; i < (int)b.size(); ++i) buf2[i].a = b[i].a;
for (int i = (int)b.size(); i < M; ++i) buf2[i].a = 0;
ntt(buf1, M);
ntt(buf2, M);
for (int i = 0; i < M; ++i)
buf1[i].a = mint::reduce(uint64_t(buf1[i].a) * buf2[i].a);
intt(buf1, M, false);
vector<mint> s(l);
mint invm = modinv(mint(M));
for (int i = 0; i < l; ++i) s[i] = buf1[i] * invm;
return s;
}
void ntt_doubling(vector<mint> &a) {
int M = (int)a.size();
for (int i = 0; i < M; i++) buf1[i].a = a[i].a;
intt(buf1, M);
mint r = 1, zeta = modpow(mint(pr),(mint::get_mod() - 1) / (M << 1));
for (int i = 0; i < M; i++) buf1[i] *= r, r *= zeta;
ntt(buf1, M);
a.resize(2 * M);
for (int i = 0; i < M; i++) a[M + i].a = buf1[i].a;
}
};
// for garner
static constexpr int m0 = 167772161;
static constexpr int m1 = 469762049;
static constexpr int m2 = 754974721;
using mint0 = MontgomeryModInt<m0>;
using mint1 = MontgomeryModInt<m1>;
using mint2 = MontgomeryModInt<m2>;
static constexpr int r01 = 104391568;
static constexpr int r02 = 323560596;
static constexpr int r12 = 399692502;
static constexpr int r02r12 = 190329765;
static constexpr i64 w1 = m0;
static constexpr i64 w2 = i64(m0) * m1;
using mint998 = MontgomeryModInt<998244353>;
NumberTheoreticTransform<mint998> ntt998;
NumberTheoreticTransform<mint0> ntt0;
NumberTheoreticTransform<mint1> ntt1;
NumberTheoreticTransform<mint2> ntt2;
// small case (T = mint, long long)
template<class T> vector<T> naive_mul
(const vector<T> &A, const vector<T> &B) {
if (A.empty() || B.empty()) return {};
int N = (int)A.size(), M = (int)B.size();
vector<T> res(N + M - 1);
for (int i = 0; i < N; ++i)
for (int j = 0; j < M; ++j)
res[i + j] += A[i] * B[j];
return res;
}
// mint
template<class mint>
vector<mint> mul(vector<mint> A,vector<mint> B) {
if (A.empty() || B.empty()) return {};
int n = int(A.size()), m = int(B.size());
if (min(n, m) < 30) return naive_mul(A, B);
int MOD = A[0].getmod();
if (MOD == 998244353) {
vector<mint998> a(n),b(m);
for(int i=0;i<n;i++) a[i]=mint998(A[i].get());
for(int i=0;i<m;i++) b[i]=mint998(B[i].get());
vector<mint998> c=ntt998.multiply(a,b);
vector<mint> res(n+m-1);
for(int i=0;i<n+m-1;i++) res[i]=c[i].get();
return res;
}
vector<mint0> a0(n), b0(m);
vector<mint1> a1(n), b1(m);
vector<mint2> a2(n), b2(m);
for (int i = 0; i < n; ++i)
a0[i] = mint0(A[i].get()), a1[i] = mint1(A[i].get()), a2[i] = mint2(A[i].get());
for (int i = 0; i < m; ++i)
b0[i] = mint0(B[i].get()), b1[i] = mint1(B[i].get()), b2[i] = mint2(B[i].get());
static const int W1 = w1%MOD, W2 = w2%MOD;
vector<mint0> c0=ntt0.multiply(a0,b0);
vector<mint1> c1=ntt1.multiply(a1,b1);
vector<mint2> c2=ntt2.multiply(a2,b2);
vector<mint> res(n + m - 1);
for (int i = 0; i < n + m - 1; ++i) {
int n1 = c1[i].get(), n2 = c2[i].get(), a = c0[i].get();
int b = i64(n1 + m1 - a) * r01 % m1;
int c = (i64(n2 + m2 - a) * r02r12 + i64(m2 - b) * r12) % m2;
res[i] = mint(i64(a) + i64(b) * W1 + i64(c) * W2);
}
return res;
}
};
// Formal Power Series
template <typename mint> struct FPS : vector<mint> {
using vector<mint>::vector;
/*
template<class...Args>
FPS(Args...args) : vector<mint>(args...){}
*/
// constructor
FPS(const vector<mint>& r) : vector<mint>(r) {}
// core operator
inline FPS pre(int siz) const {
return FPS(begin(*this), begin(*this) + min((int)this->size(), siz));
}
inline FPS rev() const {
FPS res = *this;
reverse(begin(res), end(res));
return res;
}
inline FPS& normalize() {
while (!this->empty() && this->back() == 0) this->pop_back();
return *this;
}
// basic operator
inline FPS operator - () const noexcept {
FPS res = (*this);
for (int i = 0; i < (int)res.size(); ++i) res[i] = -res[i];
return res;
}
inline FPS operator + (const mint& v) const { return FPS(*this) += v; }
inline FPS operator + (const FPS& r) const { return FPS(*this) += r; }
inline FPS operator - (const mint& v) const { return FPS(*this) -= v; }
inline FPS operator - (const FPS& r) const { return FPS(*this) -= r; }
inline FPS operator * (const mint& v) const { return FPS(*this) *= v; }
inline FPS operator * (const FPS& r) const { return FPS(*this) *= r; }
inline FPS operator / (const mint& v) const { return FPS(*this) /= v; }
inline FPS operator << (int x) const { return FPS(*this) <<= x; }
inline FPS operator >> (int x) const { return FPS(*this) >>= x; }
inline FPS& operator += (const mint& v) {
if (this->empty()) this->resize(1);
(*this)[0] += v;
return *this;
}
inline FPS& operator += (const FPS& r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); ++i) (*this)[i] += r[i];
return this->normalize();
}
inline FPS& operator -= (const mint& v) {
if (this->empty()) this->resize(1);
(*this)[0] -= v;
return *this;
}
inline FPS& operator -= (const FPS& r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); ++i) (*this)[i] -= r[i];
return this->normalize();
}
inline FPS& operator *= (const mint& v) {
for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= v;
return *this;
}
inline FPS& operator *= (const FPS& r) {
return *this = NTT::ntt998.multiply((*this), r);
}
inline FPS& operator /= (const mint& v) {
assert(v != 0);
mint iv = modinv(v);
for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= iv;
return *this;
}
inline FPS& operator <<= (int x) {
FPS res(x, 0);
res.insert(res.end(), begin(*this), end(*this));
return *this = res;
}
inline FPS& operator >>= (int x) {
FPS res;
res.insert(res.end(), begin(*this) + x, end(*this));
return *this = res;
}
inline mint eval(const mint& v){
mint res = 0;
for (int i = (int)this->size()-1; i >= 0; --i) {
res *= v;
res += (*this)[i];
}
return res;
}
inline friend FPS gcd(const FPS& f, const FPS& g) {
if (g.empty()) return f;
return gcd(g, f % g);
}
// advanced operation
// df/dx
inline friend FPS diff(const FPS& f) {
int n = (int)f.size();
FPS res(n-1);
for (int i = 1; i < n; ++i) res[i-1] = f[i] * i;
return res;
}
// \int f dx
inline friend FPS integral(const FPS& f) {
int n = (int)f.size();
FPS res(n+1, 0);
for (int i = 0; i < n; ++i) res[i+1] = f[i] / (i+1);
return res;
}
// inv(f), f[0] must not be 0
inline friend FPS inv(const FPS& f, int deg) {
assert(f[0] != 0);
if (deg < 0) deg = (int)f.size();
FPS res({mint(1) / f[0]});
for (int i = 1; i < deg; i <<= 1) {
res = (res + res - res * res * f.pre(i << 1)).pre(i << 1);
}
res.resize(deg);
return res;
}
inline friend FPS inv(const FPS& f) {
return inv(f, f.size());
}
// division, r must be normalized (r.back() must not be 0)
inline FPS& operator /= (const FPS& r) {
const int n=(*this).size(),m=r.size();
if(n<m){
(*this).clear();
return *this;
}
assert(r.back() != 0);
this->normalize();
if (this->size() < r.size()) {
this->clear();
return *this;
}
int need = (int)this->size() - (int)r.size() + 1;
*this = ((*this).rev().pre(need) * inv(r.rev(), need)).pre(need).rev();
return *this;
}
inline FPS& operator %= (const FPS &r) {
const int n=(*this).size(),m=r.size();
if(n<m) return (*this);
assert(r.back() != 0);
this->normalize();
FPS q = (*this) / r;
return *this -= q * r;
}
inline FPS operator / (const FPS& r) const { return FPS(*this) /= r; }
inline FPS operator % (const FPS& r) const { return FPS(*this) %= r; }
// log(f) = \int f'/f dx, f[0] must be 1
inline friend FPS log(const FPS& f, int deg) {
assert(f[0] == 1);
FPS res = integral((diff(f) * inv(f, deg)).pre(deg-1));
return res;
}
inline friend FPS log(const FPS& f) {
return log(f, f.size());
}
// exp(f), f[0] must be 0
inline friend FPS exp(const FPS& f, int deg) {
assert(f[0] == 0);
FPS res(1, 1);
for (int i = 1; i < deg; i <<= 1) {
res = res * (f.pre(i<<1) - log(res, i<<1) + 1).pre(i<<1);
}
res.resize(deg);
return res;
}
inline friend FPS exp(const FPS& f) {
return exp(f, f.size());
}
// pow(f) = exp(e * log f)
inline friend FPS pow(const FPS& f, long long e, int deg) {
long long i = 0;
while (i < (int)f.size() && f[i] == 0) ++i;
if (i == (int)f.size()) return FPS(deg, 0);
if (i * e >= deg) return FPS(deg, 0);
mint k = f[i];
FPS res = exp(log((f >> i) / k, deg) * e, deg) * modpow(k, e) << (e * i);
res.resize(deg);
return res;
}
inline friend FPS pow(const FPS& f, long long e) {
return pow(f, e, f.size());
}
// sqrt(f), f[0] must be 1
inline friend FPS sqrt_base(const FPS& f, int deg) {
assert(f[0] == 1);
mint inv2 = mint(1) / 2;
FPS res(1, 1);
for (int i = 1; i < deg; i <<= 1) {
res = (res + f.pre(i << 1) * inv(res, i << 1)).pre(i << 1);
for (mint& x : res) x *= inv2;
}
res.resize(deg);
return res;
}
inline friend FPS sqrt_base(const FPS& f) {
return sqrt_base(f, f.size());
}
FPS taylor_shift(mint c) const {
int n = (int) this->size();
vector<mint> fact(n), rfact(n);
fact[0] = rfact[0] = mint(1);
for(int i = 1; i < n; i++) fact[i] = fact[i - 1] * mint(i);
rfact[n - 1] = mint(1) / fact[n - 1];
for(int i = n - 1; i > 1; i--) rfact[i - 1] = rfact[i] * mint(i);
FPS p(*this);
for(int i = 0; i < n; i++) p[i] *= fact[i];
p = p.rev();
FPS bs(n, mint(1));
for(int i = 1; i < n; i++) bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1];
p = (p * bs).pre(n);
p = p.rev();
for(int i = 0; i < n; i++) p[i] *= rfact[i];
return p;
}
};
template <typename mint> FPS<mint> product(vector<FPS<mint>> a){
int siz=1;
while(siz<int(a.size())){
siz<<=1;
}
vector<FPS<mint>> res(siz*2-1,{1});
for(int i=0;i<int(a.size());++i){
res[i+siz-1]=a[i];
}
for(int i=siz-2;i>=0;--i){
res[i]=res[2*i+1]*res[2*i+2];
}
return res[0];
}
template<typename mint> FPS<mint> inv_sum(vector<FPS<mint>> f){
int siz=1;
while(siz<int(f.size())){
siz<<=1;
}
vector<FPS<mint>> mol(siz*2-1),dem(siz*2-1,{1});
for(size_t i=0;i<f.size();++i){
mol[i+siz-1]={1};
dem[i+siz-1]=f[i];
}
for(int i=siz-2;i>=0;--i){
dem[i]=dem[2*i+1]*dem[2*i+2];
mol[i]=mol[2*i+1]*dem[2*i+2]+mol[2*i+2]*dem[2*i+1];
}
mol[0]*=inv(dem[0]);
return mol[0];
}
template <typename mint> FPS<mint> rev(FPS<mint> p) { reverse(p.begin(),p.end()); return p; }
template <typename mint> FPS<mint> RSZ(FPS<mint> p, int x) { p.resize(x); return p; }
//fast Input by yosupo
#include <unistd.h>
#include <algorithm>
#include <array>
#include <cassert>
#include <cctype>
#include <cstring>
#include <sstream>
#include <string>
#include <type_traits>
#include <vector>
namespace fastio{
/*
quote from yosupo's submission in Library Checker
*/
int bsr(unsigned int n) {
return 8 * (int)sizeof(unsigned int) - 1 - __builtin_clz(n);
}
// @param n `1 <= n`
// @return maximum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsr(unsigned long n) {
return 8 * (int)sizeof(unsigned long) - 1 - __builtin_clzl(n);
}
// @param n `1 <= n`
// @return maximum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsr(unsigned long long n) {
return 8 * (int)sizeof(unsigned long long) - 1 - __builtin_clzll(n);
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsr(unsigned __int128 n) {
unsigned long long low = (unsigned long long)(n);
unsigned long long high = (unsigned long long)(n >> 64);
return high ? 127 - __builtin_clzll(high) : 63 - __builtin_ctzll(low);
}
namespace internal {
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral =
typename std::conditional<std::is_integral<T>::value ||
internal::is_signed_int128<T>::value ||
internal::is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
template <class T>
using is_integral_t = std::enable_if_t<is_integral<T>::value>;
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
struct Scanner {
public:
Scanner(const Scanner&) = delete;
Scanner& operator=(const Scanner&) = delete;
Scanner(FILE* fp) : fd(fileno(fp)) {}
void read() {}
template <class H, class... T> void read(H& h, T&... t) {
bool f = read_single(h);
assert(f);
read(t...);
}
int read_unsafe() { return 0; }
template <class H, class... T> int read_unsafe(H& h, T&... t) {
bool f = read_single(h);
if (!f) return 0;
return 1 + read_unsafe(t...);
}
int close() { return ::close(fd); }
private:
static constexpr int SIZE = 1 << 15;
int fd = -1;
std::array<char, SIZE + 1> line;
int st = 0, ed = 0;
bool eof = false;
bool read_single(std::string& ref) {
if (!skip_space()) return false;
ref = "";
while (true) {
char c = top();
if (c <= ' ') break;
ref += c;
st++;
}
return true;
}
bool read_single(double& ref) {
std::string s;
if (!read_single(s)) return false;
ref = std::stod(s);
return true;
}
template <class T,
std::enable_if_t<std::is_same<T, char>::value>* = nullptr>
bool read_single(T& ref) {
if (!skip_space<50>()) return false;
ref = top();
st++;
return true;
}
template <class T,
internal::is_signed_int_t<T>* = nullptr,
std::enable_if_t<!std::is_same<T, char>::value>* = nullptr>
bool read_single(T& sref) {
using U = internal::to_unsigned_t<T>;
if (!skip_space<50>()) return false;
bool neg = false;
if (line[st] == '-') {
neg = true;
st++;
}
U ref = 0;
do {
ref = 10 * ref + (line[st++] & 0x0f);
} while (line[st] >= '0');
sref = neg ? -ref : ref;
return true;
}
template <class U,
internal::is_unsigned_int_t<U>* = nullptr,
std::enable_if_t<!std::is_same<U, char>::value>* = nullptr>
bool read_single(U& ref) {
if (!skip_space<50>()) return false;
ref = 0;
do {
ref = 10 * ref + (line[st++] & 0x0f);
} while (line[st] >= '0');
return true;
}
bool reread() {
if (ed - st >= 50) return true;
if (st > SIZE / 2) {
std::memmove(line.data(), line.data() + st, ed - st);
ed -= st;
st = 0;
}
if (eof) return false;
auto u = ::read(fd, line.data() + ed, SIZE - ed);
if (u == 0) {
eof = true;
line[ed] = '\0';
u = 1;
}
ed += int(u);
line[ed] = char(127);
return true;
}
char top() {
if (st == ed) {
bool f = reread();
assert(f);
}
return line[st];
}
template <int TOKEN_LEN = 0>
bool skip_space() {
while (true) {
while (line[st] <= ' ') st++;
if (ed - st > TOKEN_LEN) return true;
if (st > ed) st = ed;
for (auto i = st; i < ed; i++) {
if (line[i] <= ' ') return true;
}
if (!reread()) return false;
}
}
};
//fast Output by ei1333
/**
* @brief Printer(高速出力)
*/
struct Printer {
public:
explicit Printer(FILE *fp) : fp(fp) {}
~Printer() { flush(); }
template< bool f = false, typename T, typename... E >
void write(const T &t, const E &... e) {
if(f) write_single(' ');
write_single(t);
write< true >(e...);
}
template< typename... T >
void writeln(const T &...t) {
write(t...);
write_single('\n');
}
void flush() {
fwrite(line, 1, st - line, fp);
st = line;
}
private:
FILE *fp = nullptr;
static constexpr size_t line_size = 1 << 16;
static constexpr size_t int_digits = 20;
char line[line_size + 1] = {};
char small[32] = {};
char *st = line;
template< bool f = false >
void write() {}
void write_single(const char &t) {
if(st + 1 >= line + line_size) flush();
*st++ = t;
}
template< typename T, enable_if_t< is_integral< T >::value, int > = 0 >
void write_single(T s) {
if(st + int_digits >= line + line_size) flush();
if(s == 0) {
write_single('0');
return;
}
if(s < 0) {
write_single('-');
s = -s;
}
char *mp = small + sizeof(small);
typename make_unsigned< T >::type y = s;
size_t len = 0;
while(y > 0) {
*--mp = y % 10 + '0';
y /= 10;
++len;
}
memmove(st, mp, len);
st += len;
}
void write_single(const string &s) {
for(auto &c : s) write_single(c);
}
void write_single(const char *s) {
while(*s != 0) write_single(*s++);
}
template< typename T >
void write_single(const vector< T > &s) {
for(size_t i = 0; i < s.size(); i++) {
if(i) write_single(' ');
write_single(s[i]);
}
}
};
}; //namespace fastio
using mint=MontgomeryModInt<998244353>;
int main(){
fastio::Scanner sc(stdin);
fastio::Printer pr(stdout);
#define in(...) sc.read(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define out(...) pr.write(__VA_ARGS__)
#define outln(...) pr.writeln(__VA_ARGS__)
#define outspace(...) pr.write(__VA_ARGS__);pr.write(' ')
#define rall(v) (v).rbegin(), (v).rend()
#define fi first
#define se second
/*
草
好き
*/
INT(t);
while(t--){
LL(n,x);
if(x==1){
mint ans=n/2+(n%2?1:0);
outln(ans.get());
}else{
mint ans=n/(x+1)*((x+1)/2+((x+1)%2?1:0));
outln(ans.get());
}
}
}