結果
| 問題 | No.1938 Lagrange Sum |
| ユーザー |
👑  potato167
|
| 提出日時 | 2023-03-31 02:03:21 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 144 ms / 3,000 ms |
| コード長 | 32,527 bytes |
| コンパイル時間 | 4,599 ms |
| コンパイル使用メモリ | 269,048 KB |
| 実行使用メモリ | 8,576 KB |
| 最終ジャッジ日時 | 2024-09-22 09:31:26 |
| 合計ジャッジ時間 | 8,275 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
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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 | 144 ms
8,576 KB |
| testcase_01 | AC | 144 ms
8,576 KB |
| testcase_02 | AC | 144 ms
8,576 KB |
| testcase_03 | AC | 2 ms
6,940 KB |
| testcase_04 | AC | 2 ms
6,940 KB |
| testcase_05 | AC | 107 ms
7,296 KB |
| testcase_06 | AC | 127 ms
7,552 KB |
| testcase_07 | AC | 3 ms
6,940 KB |
| testcase_08 | AC | 47 ms
6,940 KB |
| testcase_09 | AC | 24 ms
6,940 KB |
| testcase_10 | AC | 143 ms
8,316 KB |
| testcase_11 | AC | 49 ms
6,940 KB |
| testcase_12 | AC | 143 ms
8,192 KB |
| testcase_13 | AC | 143 ms
8,320 KB |
| testcase_14 | AC | 76 ms
6,944 KB |
| testcase_15 | AC | 17 ms
6,944 KB |
| testcase_16 | AC | 139 ms
7,936 KB |
| testcase_17 | AC | 74 ms
6,940 KB |
| testcase_18 | AC | 74 ms
6,940 KB |
| testcase_19 | AC | 141 ms
8,192 KB |
| testcase_20 | AC | 141 ms
8,040 KB |
| testcase_21 | AC | 11 ms
6,944 KB |
| testcase_22 | AC | 2 ms
6,940 KB |
| testcase_23 | AC | 10 ms
6,944 KB |
| testcase_24 | AC | 139 ms
8,064 KB |
| testcase_25 | AC | 2 ms
6,940 KB |
| testcase_26 | AC | 2 ms
6,940 KB |
| testcase_27 | AC | 2 ms
6,940 KB |
ソースコード
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
using std::cout;
using std::cin;
using std::endl;
using ll=long long;
using ld=long double;
ll ILL=2167167167167167167;
const int INF=2100000000;
const int mod=998244353;
#define rep(i,a,b) for (ll i=a;i<b;i++)
#define all(p) p.begin(),p.end()
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,const T &b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";}
template<class T> void vec_out(vector<T> &p){for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}
template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
template<class T> T vec_sum(vector<T> &a){assert(!a.empty());T ans=a[0]-a[0];for(auto &x:a) ans+=x;return ans;}
ll jyo(ll x,ll y,ll z){
ll H=y; //ここから
ll a=1,b=(x%z+z)%z,c=1;
while(H>0){
a*=2;
if(H%a!=0){
H-=a/2;
c*=b;
c%=z;
}
b*=b;
b%=z;
} //ここまで
return c;
}
namespace atcoder {
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(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 (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
namespace internal {
#ifndef _MSC_VER
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 ||
is_signed_int128<T>::value ||
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;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<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,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
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
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
namespace internal {
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for (int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for (int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 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)(mint::mod() + l.val() - r.val()) *
inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) {
if (n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
const std::vector<long long>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
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 constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
// B = 2^63, -B <= x, r(real value) < B
// (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
// r = c1[i] (mod MOD1)
// focus on MOD1
// r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
// r = x,
// x - M' + (0 or 2B),
// x - 2M' + (0, 2B or 4B),
// x - 3M' + (0, 2B, 4B or 6B) (without mod!)
// (r - x) = 0, (0)
// - M' + (0 or 2B), (1)
// -2M' + (0 or 2B or 4B), (2)
// -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
// we checked that
// ((1) mod MOD1) mod 5 = 2
// ((2) mod MOD1) mod 5 = 3
// ((3) mod MOD1) mod 5 = 4
long long diff =
c1[i] - internal::safe_mod((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;
}
} // namespace atcoder
using namespace atcoder;
//参考 https://nyaannyaan.github.io/library/fps/formal-power-series.hpp.html
namespace po167{
long long rev(long long a,long long MOD){
long long D=1,C=MOD-2;
while(C){
if(C&1) D=(D*a)%MOD;
C>>=1;
a=(a*a)%MOD;
}
return D;
}
template <unsigned int mod = 998244353>
std::vector<long long> add_Polynomial(std::vector<long long> &p,std::vector<long long> &q){
std::vector<long long> r(std::max(p.size(),q.size()));
for(int i=0;i<(int)r.size();i++){
if((int)p.size()>i) r[i]=p[i];
if((int)q.size()>i) r[i]=(r[i]+q[i])%mod;
}
return r;
}
template <unsigned int mod = 998244353>
std::vector<long long> sub_Polynomial(std::vector<long long> &p,std::vector<long long> &q){
std::vector<long long> r(std::max(p.size(),q.size()));
for(int i=0;i<(int)r.size();i++){
if((int)p.size()>i) r[i]=p[i];
if((int)q.size()>i) r[i]=(r[i]-q[i]);
if(r[i]<0) r[i]=(r[i]%mod+mod)%mod;
}
return r;
}
template <unsigned int mod = 998244353>
long long substitution_Polynomial(std::vector<long long> &p,long long x){
long long ans=0;
long long D=1;
for(int i=0;i<p.size();i++){
ans=(ans+(D*p[i])%mod)%mod;
D=(D*x)%mod;
}
return ans;
}
template <unsigned int mod = 998244353>
std::vector<long long> differential_Polynomial(std::vector<long long> &p){
int N=p.size();
std::vector<long long> r(N);
for(int i=1;i<N;i++){
r[i-1]=((long long)(i)*p[i])%mod;
}
return r;
}
template <unsigned int mod = 998244353>
std::vector<long long> Integral_Polynomial(std::vector<long long> &p){
int N=p.size();
std::vector<long long> r(1+N);
std::vector<long long> rev(N+1,1);
for(int i=0;i<N;i++){
if(i+1>1){
rev[i+1]=(mod-((mod/(i+1))*rev[mod%(i+1)])%mod)%mod;
}
r[i+1]=(rev[i+1]*p[i])%mod;
}
return r;
}
template <class T>
std::vector<T> slice_vec(std::vector<T> &p,int S){
if(S>=(int)(p.size())) return p;
std::vector<T> r(S);
for(int i=0;i<S;i++) r[i]=p[i];
return r;
}
// return f^{-1} mod x^{L}
// https://judge.yosupo.jp/submission/79004
template <unsigned int mod = 998244353>
std::vector<long long> inv_FPS(int N,int L,std::vector<long long> &p){
assert((int)p.size()==N);
assert(0<N);
assert(p[0]%mod!=0);
std::vector<long long> q={1},tmp,tmp2;
long long D=p[0];
long long C=mod-2;
while(C){
if(C&1){
q[0]=(q[0]*D)%mod;
}
C>>=1;
D=(D*D)%mod;
}
int S=1;
while(S<L){
S*=2;
tmp.assign(S,0);
for(int i=0;i<std::min((int)(p.size()),S);i++) tmp[i]=p[i];
tmp2=convolution<mod>(tmp,convolution<mod>(q,q));
for(int i=0;i<S;i++){
if(i*2<S) tmp[i]=(2ll*q[i]-tmp2[i]+mod)%mod;
else tmp[i]=(-tmp2[i]+mod)%mod;
}
swap(tmp,q);
}
std::vector<long long> ans(S);
for(int i=0;i<S;i++) ans[i]=q[i];
return ans;
}
// return log f(x)
// https://judge.yosupo.jp/submission/79008
template <unsigned int mod = 998244353>
std::vector<long long> log_FPS(int N,int L,std::vector<long long> &p){
assert(p[0]==1);
auto tmp=convolution<mod>(differential_Polynomial<mod>(p),inv_FPS<mod>(N,L,p));
auto tmp3=Integral_Polynomial<mod>(tmp);
return slice_vec(tmp3,L);
}
// return e^{f(x)}
template <unsigned int mod = 998244353>
std::vector<long long> exp_FPS(int N,int L,std::vector<long long> &p){
assert((int)p.size()==N);
assert(0<N);
assert(p[0]%mod==0);
std::vector<long long> q={1},tmp,tmp2,tmp3;
int S=1;
while(S<L){
S*=2;
tmp=slice_vec(p,S);
tmp2=log_FPS<mod>(S/2,S,q);
tmp3=sub_Polynomial<mod>(tmp,tmp2);
tmp3[0]++;
tmp=convolution<mod>(q,tmp3);
for(int i=0;i<S;i++){
if(i==(int)(q.size())) q.push_back(tmp[i]);
else q[i]=tmp[i];
}
}
std::vector<long long> ans(S);
for(int i=0;i<S;i++) ans[i]=q[i];
return ans;
}
//if all zero:
// return {0}
std::vector<long long> zero_cut(std::vector<long long> &p){
int ind=0;
for(int i=0;i<(int)(p.size());i++){
if(p[i]!=0) ind=i;
}
return slice_vec(p,ind+1);
}
//return {a,b} (p=aq+b)
//https://judge.yosupo.jp/submission/79020
template <unsigned int mod = 998244353>
std::pair<std::vector<long long>,std::vector<long long>> div_FPS(std::vector<long long> &p,std::vector<long long> &q){
int N=p.size(),M=q.size();
if(N<M){
return {{0},p};
}
auto f=p,g=q;
std::reverse(f.begin(),f.end());
std::reverse(g.begin(),g.end());
auto tmp=convolution<mod>(f,inv_FPS(M,N-M+1,g));
auto ans1=slice_vec(tmp,N-M+1);
std::reverse(ans1.begin(),ans1.end());
tmp=convolution(ans1,q);
std::vector<long long> ans2(M-1);
for(int i=0;i<M-1;i++) ans2[i]=(p[i]-tmp[i]+mod)%mod;
return std::make_pair(zero_cut(ans1),zero_cut(ans2));
}
//return [f(p[0]),f(p[1])...f(p[M-1])]
//https://judge.yosupo.jp/submission/79035
template <unsigned int mod = 998244353>
std::vector<long long> Multipoint_Evaluation(std::vector<long long> f,std::vector<long long>p){
int M=p.size();
if(M==0){
return {};
}
std::vector<int> size={M};
int ind=0;
while(size[ind]!=1){
size.push_back((size[ind]+1)/2);
ind++;
}
ind++;
std::vector<std::vector<std::vector<long long>>> divisor(ind),remain(ind);
for(int i=0;i<ind;i++){
divisor[i].resize(size[i]);
if(i==0){
for(int j=0;j<M;j++){
divisor[i][j]={mod-p[j],1};
}
}else{
for(int j=0;j<size[i];j++){
if(j!=size[i]-1||size[i-1]%2==0){
divisor[i][j]=convolution<mod>(divisor[i-1][j*2],divisor[i-1][j*2+1]);
}else{
divisor[i][j]=divisor[i-1][size[i-1]-1];
}
}
}
}
for(int i=ind-1;i>=0;i--){
remain[i].resize(size[i]);
if(i==ind-1){
remain[i][0]=div_FPS<mod>(f,divisor[ind-1][0]).second;
}else{
for(int j=0;j<size[i];j++){
if(j!=size[i]-1||size[i]%2==0){
remain[i][j]=div_FPS(remain[i+1][j/2],divisor[i][j]).second;
}else{
remain[i][j]=remain[i+1][j/2];
}
}
}
}
std::vector<long long> ans(M);
for(int i=0;i<M;i++) ans[i]=remain[0][i][0];
return ans;
}
template <unsigned int mod = 998244353>
std::vector<long long> multiplication_FPS(std::vector<std::vector<long long>> &p){
std::queue<std::vector<long long>> pq;
int N=p.size();
for(int i=0;i<N;i++) pq.push(p[i]);
for(int i=1;i<N;i++){
auto l=pq.front();
pq.pop();
auto r=pq.front();
pq.pop();
pq.push(convolution<mod>(l,r));
}
return pq.front();
}
struct frac_fps{
std::vector<long long> ch;
std::vector<long long> mo;
};
template <unsigned int mod = 998244353>
frac_fps add_frac_fps(frac_fps &l,frac_fps &r){
auto tmp1=convolution<mod>(l.ch,r.mo);
auto tmp2=convolution<mod>(l.mo,r.ch);
return {add_Polynomial<mod>(tmp1,tmp2),convolution<mod>(l.mo,r.mo)};
}
template <unsigned int mod = 998244353>
std::vector<long long> Polynomial_Interpolation(std::vector<long long> &x,std::vector<long long> &y){
int N=x.size();
assert(x.size()==y.size());
std::vector<std::vector<long long>> p(N);
for(int i=0;i<N;i++){
p[i]={(mod-x[i])%mod,1};
}
auto tmp1=multiplication_FPS<mod>(p);
auto div=differential_Polynomial<mod>(tmp1);
auto val=Multipoint_Evaluation<mod>(div,x);
std::queue<frac_fps> q;
for(int i=0;i<N;i++) q.push({{y[i]},{(mod-(val[i]*x[i])%mod)%mod,val[i]}});
for(int i=1;i<N;i++){
frac_fps l=q.front();
q.pop();
frac_fps r=q.front();
q.pop();
q.push(add_frac_fps<mod>(l,r));
}
long long D=1;
auto ans=q.front().ch;
for(int i=0;i<N;i++){
D=(D*val[i])%mod;
}
D=rev(D,mod);
for(int i=0;i<N;i++) ans[i]=(ans[i]*D)%mod;
return ans;
}
}
void solve();
// oddloop
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int t=1;
//cin>>t;
rep(i,0,t) solve();
}
void solve(){
ll N,X;
cin>>N>>X;
vector<ll> x(N),y(N);
rep(i,0,N) cin>>x[i]>>y[i];
rep(i,0,N){
if(X!=x[i]) continue;
vector<ll> p,q;
rep(j,0,N){
if(i!=j) p.push_back(x[j]),q.push_back(y[j]);
}
ll ans=0;
auto v=po167::Polynomial_Interpolation(p,q);
for(int i=N-2;i>=0;i--){
ans=(ans*X)%mod;
ans=(ans+v[i])%mod;
}
ans=(ans+y[i]*(N-1))%mod;
cout<<(ans+mod)%mod<<"\n";
return;
}
ll base=0,U=0;
rep(i,0,N){
ll A=(X-x[i]),B=-x[i];
A=jyo(A,mod-2,mod);
U=(U+A)%mod;
base=(base+A*B)%mod;
}
rep(i,0,N){
ll tmp=(x[i]*U)%mod;
y[i]=(y[i]*(base+tmp))%mod;
}
auto v=po167::Polynomial_Interpolation(x,y);
ll ans=0;
for(int i=N-1;i>=0;i--){
ans=(ans*X)%mod;
ans=(ans+v[i])%mod;
}
cout<<(ans+mod)%mod<<"\n";
}