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;
}

GOLDEN GLOBES WINNERS… DEVELOPING…

The Golden Globes 2026: Live Winners List is Developing...

Can octopus get attached...

Do Octopuses Form Genuine Bonds with Humans? The Nuanced...

News From Nancy 1/9/2026...

Five Years After the Insurrection: Reflecting on January 6th...

OpenAI Hires Co-Founders of...

OpenAI Snaps Up Convogo Co-Founders, Bolstering Expertise in AI...

Do ferrets cough up...

Understanding Ferret Health: Do Ferrets Cough Up Hairballs? For many...

Lenovo goes all in...

Lenovo's AI Leap at CES 2026: The Future Is...

GOLDEN GLOBES WINNERS… DEVELOPING…

The Golden Globes 2026: Live Winners List is Developing as Hollywood’s Biggest Night Unfolds The curtain has officially risen on the Golden Globes 2026, marking...

Can octopus get attached to humans?

Do Octopuses Form Genuine Bonds with Humans? The Nuanced Answer The question of whether an octopus can genuinely attach itself to a human has captivated...

News From Nancy 1/9/2026 — Save Our Health Care

Five Years After the Insurrection: Reflecting on January 6th and the Fight for Health Care The latest update from the “News From Nancy” series, dated...

OpenAI Hires Co-Founders of AI-Powered Tool Convogo

OpenAI Snaps Up Convogo Co-Founders, Bolstering Expertise in AI Coaching and HR The global race for top artificial intelligence talent continues to heat up, and...

Do ferrets cough up hairballs?

Understanding Ferret Health: Do Ferrets Cough Up Hairballs? For many small pet owners, the sight or sound of a cat coughing up a hairball is...

Lenovo goes all in on AI with concepts at CES 2026

Lenovo's AI Leap at CES 2026: The Future Is Conceptual CES is renowned for launching the must-have gadgets of the year, but the annual tech...

Why 99% of scientists believe in evolution

The Unanimous Truth: Why 99% of Scientists Believe in Evolution In the public discourse, the debate between evolutionary theory and creationism often appears balanced. However,...

Charles Cross agrees to four-year extension with Seahawks

Charles Cross Secures Future with Massive Four-Year Extension with Seahawks The Seattle Seahawks organization demonstrated its commitment to building a formidable foundation by securing one...

Samsung Display Unveils New OLED Tech for Robots & Wearables at CES 2026

Samsung Display Prepares to Dazzle CES 2026 with Next-Gen OLED Innovations As the tech world gears up for CES 2026, all eyes are turning toward...