Sponsors

Codeforces Round #412 (rated, Div. 1, based on VK Cup 2017 Round 3), problem: (F) Test Data Generation, Accepted Solution In C/C++

#include<bits/stdc++.h>
#define ll long long

ll multmod(ll a, ll b, ll moder){
 a = (a % moder + moder) % moder, b = (b % moder + moder) % moder;
 ll ret = 0;
 for ( ; b; b >>= 1){
 if (b & 1){
 ret = ret + a >= moder ? ret + a - moder : ret + a;
 }
 a = a << 1 > moder ? (a << 1) - moder : a << 1;
 }
 return ret;
}

template <typename T> 
class modequa{
private:
 T remain, moder;
 
public:
 modequa <T>(){}
 modequa <T>(T remain, T moder) : remain(remain), moder(moder){}
 T getremain(){return remain;}
 T getmoder(){return moder;}
 
 void setvalue(T remain, T moder){
 this -> remain = remain;
 this -> moder = moder;
 }
 
 modequa <T> crt(const modequa <T> &p){
 T gcd = moder, x = 1, y = 0;
 for (T b = p.moder, x1 = 0, y1 = 1, r, s; b; ){
 r = x, s = y;
 x = x1, y = y1, x1 = r - x1 * (gcd / b), y1 = s - y1 * (gcd / b);
 r = gcd % b, gcd = b, b = r;
 }
 if ((p.remain - remain) % gcd) return modequa <T>(0, 0);
 T lcm = moder / gcd * p.moder;
 T ans = (p.remain - remain) / gcd;
 ans = multmod(multmod(ans, x, lcm), moder, lcm);
 ans += remain;
 ans += ans < 0 ? lcm : ans >= lcm ? -lcm : 0;
 return modequa <T>(ans, lcm);
 }
};

// Èç¹ûÄ£Êý²»ÊÇÖÊÊý£¬ÄÇô»ù±¾¾ÍÖ»ÄÜ×ö¼Ó¼õ³ËºÍÇóµ¼ÁËorz 
class poly{
private:
 int *a;
 int length, size;
 int moder, root, invroot;
 // ³£ÓõÄÁ½×éÄ£ÊýΪ ((119 << 23) + 1, 3, 332748118) ºÍ ((479 << 21) + 1, 3, 334845270)

 int powermod(int a, int exp, int moder)const &{
 int ret = 1;
 for ( ; exp; exp >>= 1){
 if (exp & 1){
 ret = 1ll * a * ret % moder;
 }
 a = 1ll * a * a % moder;
 }
 return ret;
 }
 
 void NTT(int *a, int length, int type, int moder, int root)const &{
 int len = -1;
 for (int x = length; x; ++ len, x >>= 1);
 for(int i = 1, j = 0; i < length - 1; ++ i){
 for(int s = length; j ^= s >>= 1, ~j & s; );
 if(i < j){
 std::swap(a[i], a[j]);
 }
 }
 for (int i = 1; i <= len; ++ i){
 int unit = powermod(root, moder - 1 >> i, moder);
 for (int j = 0; j < length; j += 1 << i){
 int w = 1;
 for (int k = j, szk = 1 << i - 1; k < j + szk; ++ k){
 int s = a[k], t = 1ll * w * a[k + szk] % moder;
 a[k] = s + t >= moder ? s + t - moder : s + t;
 a[k + szk] = s - t < 0 ? s - t + moder : s - t;
 w = 1ll * w * unit % moder;
 }
 }
 }
 if (type == 1) return;
 int inv = powermod(length, moder - 2, moder);
 for (int i = 0; i < length; ++ i){
 a[i] = 1ll * a[i] * inv % moder;
 }
 }
 
 void apply(int size){
 if (!size) return;
 a = new int [size]();
 this -> size = size;
 }
 
 void destroy(){
 if (!size) return;
 delete [] a;
 a = nullptr;
 }
 
 void resize(int size){
 if (!size) return;
 int *aux = a;
 a = new int [size]();
 memcpy(a, aux, sizeof(int) * (length + 1));
 if (this -> size) delete [] aux;
 this -> size = size;
 }

public:
 poly() : length(-1), moder(0), root(0), invroot(0){a = nullptr;}
 // Èç¹ûÄ£Êý·ÇNTTÖÊÊý root ºÍ invroot Ëæ±ãÉè¾ÍºÃÀ±~ 
 poly(int length, int moder, int root, int invroot):length(length), moder(moder), root(root), invroot(invroot){apply(length + 2 << 1);}
 poly(const poly &p):length(p.length), moder(p.moder), root(p.root), invroot(p.invroot){apply(p.size); memcpy(a, p.a, sizeof(int) * (p.length + 1));}
 poly(const poly &p, int length):length(length), moder(p.moder), root(p.root), invroot(p.invroot){apply(length + 2 << 1); memcpy(a, p.a, sizeof(int) * (std::min(length, p.length) + 1));}
 ~poly(){destroy();}
 void clear(){destroy(); length = -1, size = moder = root = invroot = 0;}
 int &operator [](int n){return a[n];}
 int getlength(){return length;}
 void setmoder(int moder, int root, int invroot){this -> moder = moder, this -> root = root, this -> invroot = invroot;}
 int getmoder(){return moder;}
 
 void setlength(int length){
 if (length >= size) resize(length + 2 << 1);
 if (length >= this -> length){
 this -> length = length;
 return;
 }
 memset(a + length + 1, 0, sizeof(int) * (this -> length - length));
 this -> length = length;
 }
 
 poly &operator = (const poly &p){
 destroy();
 apply(p.size);
 length = p.length;
 moder = p.moder;
 root = p.root;
 invroot = p.invroot;
 memcpy(a, p.a, sizeof(int) * (length + 1));
 return *this;
 }
 
 // Ï൱ÓÚ³ËÒÔ x ^ dis
 poly operator << (const int &dis)const &{
 poly ret(length + dis, moder, root, invroot);
 memcpy(ret.a + dis, a, sizeof(double) * (length + 1));
 return ret;
 }
 
 // Ï൱ÓÚ³ýÒÔ x ^ dis
 poly operator >> (const int &dis)const &{
 if (dis > length) return poly(-1, moder, root, invroot);
 poly ret(length - dis, moder, root, invroot);
 memcpy(ret.a, a + dis, sizeof(int) * (ret.length + 1));
 return ret;
 }
 
 int value(int x){
 int now = 1, ret = 0;
 for (int i = 0; i <= length; ++ i){
 ret = (ret + 1ll * a[i] * now) % moder;
 now = 1ll * now * x % moder;
 }
 return ret;
 }
 
 poly operator + (const poly &p)const &{
 if (!~length) return p;
 if (!~p.length) return *this;
 poly ret(*this, std::max(length, p.length));
 for (int i = 0; i <= p.length; ++ i){
 ret.a[i] += p.a[i];
 ret.a[i] -= ret.a[i] >= moder ? moder : 0;
 }
 for ( ; ~ret.length && !ret.a[ret.length]; -- ret.length)
 ;
 return ret;
 }
 
 poly operator - (const poly &p)const &{
 if (!~length) return p;
 if (!~p.length) return *this;
 poly ret(*this, std::max(length, p.length));
 for (int i = 0; i <= p.length; ++ i){
 ret.a[i] -= p.a[i];
 ret.a[i] += ret.a[i] < 0 ? moder : 0;
 }
 for ( ; ~ret.length && !ret.a[ret.length]; -- ret.length)
 ;
 return ret;
 }
 
 poly operator - ()const &{
 poly ret(length, moder, root, invroot);
 for (int i = 0; i <= length; ++ i){
 ret.a[i] = a[i] ? moder - a[i] : 0;
 }
 return ret;
 }
 /*&
 poly operator * (const poly &p)const &{
 if (!~length || !~p.length) return poly(-1, moder, root, invroot);
 int n = length + p.length;
 int lengthret = 1;
 for ( ; lengthret <= n; lengthret <<= 1)
 ;
 int *aux = new int [lengthret]();
 int *aux1 = new int [lengthret]();
 memcpy(aux, a, sizeof(int) * (length + 1));
 memcpy(aux1, p.a, sizeof(int) * (p.length + 1));
 NTT(aux, lengthret, 1, moder, root);
 NTT(aux1, lengthret, 1, moder, root);
 for (int i = 0; i < lengthret; ++ i){
 aux[i] = 1ll * aux[i] * aux1[i] % moder;
 }
 NTT(aux, lengthret, -1, moder, invroot);
 poly ret(n, moder, root, invroot);
 memcpy(ret.a, aux, sizeof(int) * (n + 1));
 delete [] aux;
 delete [] aux1;
 return ret;
 }*/
 
 ///*-------------------- ÕâÊÇÄ£Êý·ÇNTTÖÊÊýµÄÄ£°å£¬Çë°´ÐèÈ¡ÓÃ~ ------------------------------
 poly operator *(const poly &p)const &{
 const int multmoder[2] = {(119 << 23) + 1, (479 << 21) + 1};
 const int multroot[2] = {3, 3};
 const int multinvroot[2] = {332748118, 334845270};
 if (!~length || !~p.length) return poly(-1, moder, root, invroot);
 int n = length + p.length;
 int lengthret = 1;
 for ( ; lengthret <= n; lengthret <<= 1)
 ;
 int *aux = new int [lengthret]();
 int *aux1 = new int [lengthret]();
 int *aux2 = new int [lengthret]();
 memcpy(aux, a, sizeof(int) * (length + 1));
 memcpy(aux2, p.a, sizeof(int) * (p.length + 1));
 NTT(aux, lengthret, 1, multmoder[0], multroot[0]);
 NTT(aux2, lengthret, 1, multmoder[0], multroot[0]);
 for (int i = 0; i < lengthret; ++ i){
 aux[i] = 1ll * aux[i] * aux2[i] % multmoder[0];
 }
 NTT(aux, lengthret, -1, multmoder[0], multinvroot[0]);
 memcpy(aux1, a, sizeof(int) * (length + 1));
 memset(aux2, 0, sizeof(int) * lengthret);
 memcpy(aux2, p.a, sizeof(int) * (p.length + 1));
 NTT(aux1, lengthret, 1, multmoder[1], multroot[1]);
 NTT(aux2, lengthret, 1, multmoder[1], multroot[1]);
 for (int i = 0; i < lengthret; ++ i){
 aux1[i] = 1ll * aux1[i] * aux2[i] % multmoder[1];
 }
 NTT(aux1, lengthret, -1, multmoder[1], multinvroot[1]);
 poly ret(n, moder, root, invroot);
 for(int i = 0; i <= n; ++ i){
 modequa <ll> equa(aux[i], multmoder[0]), equb(aux1[i], multmoder[1]);
 ret.a[i] = equa.crt(equb).getremain() % moder;
 }
 delete [] aux;
 delete [] aux1;
 delete [] aux2;
 return ret;
 }
 //----------------------------------------------------------------------------------------*/
 
 poly operator * (const int &p)const &{
 int q = (p % moder + moder) % moder;
 if (!q) return poly(-1, moder, root, invroot);
 poly ret(length, moder, root, invroot);
 for (int i = 0; i <= length; ++ i){
 ret.a[i] = 1ll * a[i] * q % moder;
 }
 return ret;
 }
 
 friend poly operator * (const int &q, const poly &p){return p * q;}
 poly &operator += (const poly &p){*this = *this + p; return *this;}
 poly &operator -= (const poly &p){*this = *this - p; return *this;}
 poly &operator *= (const poly &p){*this = *this * p; return *this;}
 poly &operator *= (const int &p){*this = *this * p; return *this;}
};

const int N = 100;

int maxn, maxa, moder;
int q[N];

int main(){
 scanf("%d%d%d", &maxn, &maxa, &moder);
 if (maxa == 1){
 return printf("0\n"), 0;
 }
 int cnt = 0;
 for (maxa >>= 1; maxa; maxa >>= 1){
 q[cnt ++] = maxa;
 }
 std::reverse(q, q + cnt);
 int ans = 1;
 poly a(maxn, moder, 0, 0);
 poly b(maxn, moder, 0, 0);
 a[0] = 1;
 b[1] = 1;
 for (int i = 0; i < cnt - 1; ++ i){
 poly ret1(a);
 ret1 = (ret1 + b) * (q[i] & 1 ? b : a);
 if (q[i] & 1 ? b[0] : a[0]){
 ret1 -= b;
 }
 else{
 ret1 += a;
 }
 ret1.setlength(maxn);
 poly ret2(a);
 ret2 = (ret2 + b) * (q[i] & 1 ? a : b);
 if (q[i] & 1 ? a[0] : b[0]){
 ret2 -= a;
 }
 else{
 ret2 += b;
 }
 ret2.setlength(maxn);
 if (q[i + 1] & 1){
 a = ret1;
 for (int i = 1; i <= maxn; ++ i){
 b[i] = (ret2[i] + ret1[i - 1] + ret2[i - 1]) % moder;
 }
 }
 else{
 a = ret1;
 b = ret2;
 }
 for (int i = 1; i <= maxn; i += 2){
 ans = (ans + b[i]) % moder;
 }
 }
 return printf("%d\n", ans), 0;
}

XRP Bearish Signal: Whales...

XRP Bearish Signal: Whales Offload $486 Million in Asset The...

Faraday Future Founder and...

Faraday Future Spins Off Crypto Venture: CXC10 on the...

Ice Cube Says Critical...

Ice Cube's Shocking Revelation: "War of the Worlds" Remake...

Curtis Jones to Miss...

Curtis Jones Out, But Liverpool Avoid Major Injury Concerns...

Los Angeles County child...

Los Angeles County Child Dies from Measles Complications A tragic...

NASA Says Mars Rover...

NASA's Perseverance Rover Finds Potential Biosignature on Mars In a...

XRP Bearish Signal: Whales Offload $486 Million In Asset

XRP Bearish Signal: Whales Offload $486 Million in Asset The cryptocurrency market is known for its volatility, and recent on-chain data suggests a potential bearish...

Faraday Future Founder and Co-CEO YT Jia Shares Weekly Investor Update: FF Officially Started the Spinoff Plan for the Crypto Flywheel, a Second Independently...

Faraday Future Spins Off Crypto Venture: CXC10 on the Horizon Faraday Future, the electric vehicle company, is making waves beyond its automotive ambitions. Founder...

Ice Cube Says Critical Disaster Shot Without Director Or Actors Present

Ice Cube's Shocking Revelation: "War of the Worlds" Remake Filmed Without Crew? The 2025 remake of H.G. Wells's War of the Worlds has been met...

Curtis Jones to Miss Burnley But No Other Post-Internationals Injury Concerns

Curtis Jones Out, But Liverpool Avoid Major Injury Concerns After International Break Liverpool fans can breathe a sigh of relief. While Curtis Jones will...

Los Angeles County child dies from complications caused by measles infection, public health officials say

Los Angeles County Child Dies from Measles Complications A tragic incident in Los Angeles County highlights the severe and potentially fatal consequences of measles infection,...

NASA Says Mars Rover Discovered Potential Biosignature Last Year

NASA's Perseverance Rover Finds Potential Biosignature on Mars In a groundbreaking announcement, NASA has revealed that its Perseverance rover discovered a potential biosignature in a...

Bettors Bet Big On Trump Pardoning Binance Founder Changpeng Zhao

Bettors Bet Big on Trump Pardoning Binance Founder Changpeng Zhao A surprising prediction market trend has emerged, suggesting a significant possibility of a presidential pardon...

6 Best Long-Running Sci-Fi TV Series to Binge-Watch

6 Best Long-Running Sci-Fi TV Series to Binge-Watch Science fiction television has given us some of the most imaginative and enduring stories in recent years....

Judge sentences Australian woman to life in prison for fatal mushroom poisoning of in-laws

Australian Woman Receives Life Sentence for Fatal Mushroom Poisoning Erin Patterson, an Australian woman, has been sentenced to life in prison for the fatal mushroom...