結果
| 問題 |
No.3186 Big Order
|
| ユーザー |
 GOTKAKO
|
| 提出日時 | 2025-06-21 02:56:59 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 240 ms / 2,000 ms |
| コード長 | 24,594 bytes |
| コンパイル時間 | 4,248 ms |
| コンパイル使用メモリ | 263,296 KB |
| 実行使用メモリ | 7,848 KB |
| 最終ジャッジ日時 | 2025-06-21 02:57:09 |
| 合計ジャッジ時間 | 9,228 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 35 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
//入力が必ず-mod<a<modの時.
template<const int mod>
struct modint{ //mod変更が不可能.
public:
long long v = 0;
static void setmod(int m){} //飾り.
static constexpr long long getmod(){return mod;}
modint(){v = 0;} modint(int a){v = a<0?a+mod:a;} modint(long long a){v = a<0?a+mod:a;}
modint(unsigned int a){v = a;} modint(unsigned long long a){v = a;}
long long val()const{return v;}
modint &operator=(const modint &b) = default;
modint operator+()const{return (*this);}
modint operator-()const{return modint(0)-(*this);}
modint operator+(const modint b)const{return modint(v)+=b;}
modint operator-(const modint b)const{return modint(v)-=b;}
modint operator*(const modint b)const{return modint(v)*=b;}
modint operator/(const modint b)const{return modint(v)/=b;}
modint operator+=(const modint b){
v += b.v; if(v >= mod) v -= mod;
return *this;
}
modint operator-=(const modint b){
v -= b.v; if(v < 0) v += mod;
return *this;
}
modint operator*=(const modint b){v = v*b.v%mod; return *this;}
modint operator/=(modint b){ //b!=0 mod素数が必須.
if(b == 0) assert(false);
int left = mod-2;
while(left){if(left&1) *this *= b; b *= b; left >>= 1;}
return *this;
}
modint operator++(){*this += 1; return *this;}
modint operator--(){*this -= 1; return *this;}
modint operator++(int){*this += 1; return *this;}
modint operator--(int){*this -= 1; return *this;}
bool operator==(const modint b)const{return v == b.v;}
bool operator!=(const modint b)const{return v != b.v;}
bool operator>(const modint b)const{return v > b.v;}
bool operator>=(const modint b)const{return v >= b.v;}
bool operator<(const modint b)const{return v < b.v;}
bool operator<=(const modint b)const{return v <= b.v;}
modint pow(long long n)const{
modint ret = 1,p = v;
if(n < 0) p = p.inv(),n = -n;
while(n){
if(n&1) ret *= p;
p *= p; n >>= 1;
}
return ret;
}
modint inv()const{return modint(1)/v;} //素数mod必須.
};
using mint = modint<998244353>;
namespace to_fold{
__int128_t safemod(__int128_t a,long long m){a %= m; if(a < 0) a += m; return a;}
pair<long long,long long> invgcd(long long a,long long b){
//return {gcd(a,b),x} (xa≡g(mod b))
a = safemod(a,b);
if(a == 0) return {b,0};
long long x = 0,y = 1,memob = b;
while(a){
long long q = b/a;
b -= a*q;
swap(x,y); y -= q*x;
swap(a,b);
}
if(x < 0) x += memob/b;
return {b,x};
}
template<long long mod>
long long Garner(const vector<long long> &A,const vector<long long> &M){
__int128_t mulM = 1,x = A.at(0)%M.at(0); //Mの要素のペア互いに素必須.
for(int i=1; i<A.size(); i++){
//assert(gcd(mulM,M.at(i-1)) == 1);
mulM *= M.at(i-1); //2乗がオーバーフローする時__int128_t
long long t = safemod((A.at(i)-x)*invgcd(mulM,M.at(i)).second,M.at(i));
x += t*mulM;
}
return x%mod;
}
int countzero(unsigned long long x){
if(x == 0) return 64;
else return __popcount((x&-x)-1);
}
template<typename mint>
struct fftinfo{
static bool First;
static mint g,sum_e[30],sum_ie[30]; //sum_e[i]=Π[j=0~i-1]ies[j] * es[i],sum_ie[i]=Π[i=0~j-1]es[j] * ies[i].
static mint divpow2[30]; //div[i] = 1/(2^i).
static mint Zeta[30];
fftinfo(){
if(!First) return;
First = false;
const long long mod = mint::getmod();
if(mod == 998244353) g = 3;
else if(mod == 754974721) g = 11;
else if(mod == 167772161) g = 3;
else if(mod == 469762049) g = 3;
else assert(false); //現状RE.
mint es[30],ies[30]; //es[i]^(2^(2+i))=1.
int cnt2 = countzero(mod-1);
mint e = g.pow((mod-1)>>cnt2),ie = e.inv();
for(int i=cnt2; i>=2; i--){ //e^(2^i)=1;
es[i-2] = e,e *= e;
ies[i-2] = ie,ie *= ie;
}
mint rot = 1;
for(int i=0; i<=cnt2-2; i++) sum_e[i] = es[i]*rot,rot *= ies[i];
rot = 1;
for(int i=0; i<=cnt2-2; i++) sum_ie[i] = ies[i]*rot,rot *= es[i];
mint div2n = 1,div2 = mint(1)/2;
for(int i=0; i<30; i++) divpow2[i] = div2n,div2n *= div2;
for(int i=0; i<=cnt2; i++) Zeta[i] = g.pow((mod-1)/(2<<i));
}
};
template<typename mint> bool fftinfo<mint>::First=true;
template<typename mint> mint fftinfo<mint>::g;
template<typename mint> mint fftinfo<mint>::sum_e[30];
template<typename mint> mint fftinfo<mint>::sum_ie[30];
template<typename mint> mint fftinfo<mint>::divpow2[30];
template<typename mint> mint fftinfo<mint>::Zeta[30];
template<typename mint>
void NTT(vector<mint> &A){ //ACLを超参考にしてる.
int n = A.size();
assert((n&-n) == n);
fftinfo<mint> info;
int h = countzero(n);
for(int ph=1; ph<=h; ph++){
int w = 1<<(ph-1),p = 1<<(h-ph);
mint rot = 1;
for(int s=0; s<w; s++){
int offset = s<<(h-ph+1);
for(int i=0; i<p; i++){
mint l = A.at(i+offset),r = A.at(i+offset+p)*rot;
A.at(i+offset) = l+r;
A.at(i+offset+p) = l-r;
}
rot *= info.sum_e[countzero(~(unsigned int)(s))];
}
}
}
template<typename mint>
void INTT(vector<mint> &A){
int n = A.size();
assert((n&-n) == n);
fftinfo<mint> info;
const unsigned int mod = mint::getmod();
int h = countzero(n);
for(int ph=h; ph>0; ph--){
int w = 1<<(ph-1),p = 1<<(h-ph);
mint irot = 1;
for(int s=0; s<w; s++){
int offset = s<<(h-ph+1);
for(int i=0; i<p; i++){
mint l = A.at(i+offset),r = A.at(i+offset+p);
A.at(i+offset) = l+r;
A.at(i+offset+p) = ((unsigned long long)(mod+(unsigned int)l.v-(unsigned int)r.v)*irot.v)%mod;
}
irot *= info.sum_ie[countzero(~(unsigned int)(s))];
}
}
mint divn = info.divpow2[h];
for(auto &a : A) a *= divn;
}
template<typename mint>
vector<mint> convolution(vector<mint> A,vector<mint> B){ //mintじゃないのを突っ込まないように!!!.
int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1,N = 1;
if(siza == 0 || sizb == 0) return {};
if(min(siza,sizb) <= 60){ //naive.
vector<mint> ret(sizc);
if(siza >= sizb){for(int i=0; i<siza; i++) for(int k=0; k<sizb; k++) ret.at(i+k) += A.at(i)*B.at(k);}
else{for(int i=0; i<sizb; i++) for(int k=0; k<siza; k++) ret.at(i+k) += B.at(i)*A.at(k);}
return ret;
}
while(N < sizc) N <<= 1;
A.resize(N),B.resize(N);
NTT(A); NTT(B);
for(int i=0; i<N; i++) A.at(i) *= B.at(i);
INTT(A); A.resize(sizc);
return A;
}
vector<long long> convolution_ll(const vector<long long> &A,const vector<long long> &B){ //long longに収まる範囲.
int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1;
if(siza == 0 || sizb == 0) return {};
vector<long long> ret(sizc);
if(min(siza,sizb) <= 200){ //naive 200はやばい?.
vector<long long> ret(sizc);
if(siza >= sizb){for(int i=0; i<siza; i++) for(int k=0; k<sizb; k++) ret.at(i+k) += A.at(i)*B.at(k);}
else{for(int i=0; i<sizb; i++) for(int k=0; k<siza; k++) ret.at(i+k) += B.at(i)*A.at(k);}
return ret;
}
const unsigned long long mod1 = 754974721,mod2 = 167772161,mod3 = 469762049;
const unsigned long long m1m2 = mod1*mod2,m2m3 = mod2*mod3,m3m1 = mod3*mod1,m1m2m3 = mod1*mod2*mod3;
const unsigned long long i1 = invgcd(m2m3,mod1).second,i2 = invgcd(m3m1,mod2).second,i3 = invgcd(m1m2,mod3).second;
assert(sizc <= (1<<24));
using mint1 = modint<mod1>;
using mint2 = modint<mod2>;
using mint3 = modint<mod3>;
vector<mint1> a1(siza),b1(sizb);
vector<mint2> a2(siza),b2(sizb);
vector<mint3> a3(siza),b3(sizb);
for(int i=0; i<siza; i++) a1.at(i) = A.at(i)%mod1;
for(int i=0; i<sizb; i++) b1.at(i) = B.at(i)%mod1;
vector<mint1> C1 = convolution(a1,b1);
for(int i=0; i<siza; i++) a2.at(i) = A.at(i)%mod2;
for(int i=0; i<sizb; i++) b2.at(i) = B.at(i)%mod2;
vector<mint2> C2 = convolution(a2,b2);
for(int i=0; i<siza; i++) a3.at(i) = A.at(i)%mod3;
for(int i=0; i<sizb; i++) b3.at(i) = B.at(i)%mod3;
vector<mint3> C3 = convolution(a3,b3);
vector<unsigned long long> offset = {0,0,m1m2m3,2*m1m2m3,3*m1m2m3};
for(int i=0; i<sizc; i++){
unsigned long long x = 0;
x += (C1.at(i).v*i1)%mod1*m2m3;
x += (C2.at(i).v*i2)%mod2*m3m1;
x += (C3.at(i).v*i3)%mod3*m1m2;
long long diff = C1.at(i).v-((long long)x+(long long)mod1)%mod1;
if(diff < 0) diff += mod1;
x -= offset.at(diff%5);
ret.at(i) = x;
}
return ret;
}
template<typename mint>
vector<mint> convolution_llmod(const vector<mint> &A,const vector<mint> &B){
int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1;
if(siza == 0 || sizb == 0) return {};
vector<mint> ret(sizc);
if(min(siza,sizb) <= 200){
for(int i=0; i<siza; i++) for(int k=0; k<sizb; k++) ret.at(i+k) += A.at(i)*B.at(k);
return ret;
}
const long long mod1 = 754974721,mod2 = 167772161,mod3 = 469762049;
assert(sizc <= (1<<24));
using mint1 = modint<mod1>;
using mint2 = modint<mod2>;
using mint3 = modint<mod3>;
vector<mint1> a1(siza),b1(sizb);
vector<mint2> a2(siza),b2(sizb);
vector<mint3> a3(siza),b3(sizb);
for(int i=0; i<siza; i++) a1.at(i) = A.at(i).v%mod1;
for(int i=0; i<sizb; i++) b1.at(i) = B.at(i).v%mod1;
vector<mint1> C1 = convolution(a1,b1);
for(int i=0; i<siza; i++) a2.at(i) = A.at(i).v%mod2;
for(int i=0; i<sizb; i++) b2.at(i) = B.at(i).v%mod2;
vector<mint2> C2 = convolution(a2,b2);
for(int i=0; i<siza; i++) a3.at(i) = A.at(i).v%mod3;
for(int i=0; i<sizb; i++) b3.at(i) = B.at(i).v%mod3;
vector<mint3> C3 = convolution(a3,b3);
for(int i=0; i<sizc; i++){
vector<long long> A = {C1.at(i).v,C2.at(i).v,C3.at(i).v};
vector<long long> M = {mod1,mod2,mod3};
ret.at(i) = Garner<mint::getmod()>(A,M);
}
return ret;
}
vector<int> convolution_int(const vector<int> &A,const vector<int> &B){ //intに収まる範囲.
if(A.size() == 0 || B.size() == 0) return {};
vector<int> ret;
if(min(A.size(),B.size()) <= 60){
ret.resize(A.size()+B.size()-1);
for(int i=0; i<A.size(); i++) for(int k=0; k<B.size(); k++) ret.at(i+k) += A.at(i)*B.at(k);
}
else{
using mint1 = modint<998244353>;
vector<mint1> X(A.size()),Y(B.size()),Z;
for(int i=0; i<A.size(); i++) X.at(i) = A.at(i);
for(int i=0; i<B.size(); i++) Y.at(i) = B.at(i);
Z = convolution(X,Y);
ret.resize(Z.size());
for(int i=0; i<Z.size(); i++) ret.at(i) = Z.at(i).v;
}
return ret;
}
template<typename mint>
void NTTdoubling(vector<mint> &A){ //NTTの原理を忘れているため何やってるのか意味が分からない NTT-friendly専用.
//INTT->resize(2倍）->NTTの代わりにcopy->INTT->謎の操作->NTT->push sizeが小さい時は効率悪いらしいよ.
int n = A.size();
fftinfo<mint> info;
vector<mint> B = A;
INTT(B);
mint rot = 1,zeta = info.Zeta[countzero(n)];
for(auto &v : B) v *= rot,rot *= zeta;
NTT(B); A.reserve(n<<1);
for(auto &v : B) A.push_back(v);
}
bool isNTTfriendly(long long mod){
if(mod == 998244353 || mod == 754974721 || mod == 16777216 || mod == 469762049) return true;
return false; //現状false 原子根求める機能を追加してから.
int have2 = countzero(mod-1);
return have2 >= 20;//とりあえず2^20でokとする;
}
}
using namespace to_fold;
struct bigint{
//__int128_t以上の数にも対応.
//計算量 普通O(桁数),掛け算O(桁数log桁数),割り算O(桁数log桁数)(重い).
public:
bool isMinus; //負かどうか.
vector<int> V;//絶対値.
//先頭の要素の方が小さい位 5108->{8,0,1,5}.
private:
void slide(){
for(int i=0; i<V.size(); i++){
int v = V.at(i);
int div10 = v<0?(v+1)/10-1:v/10; //÷10切り捨て.
if(div10 == 0) continue;
if(i+1==V.size()) V.push_back(0);
V.at(i+1) += div10; V.at(i) -= div10*10;
}
while(V.size() && V.back() == 0) V.pop_back();
if(V.size() == 0) isMinus = false;
}
int comp(const bigint &b){ //0->|a|<|b|,1->|a|>|b|,2->|a|==|b|.
if(V.size() < b.V.size()) return 0;
if(V.size() > b.V.size()) return 1;
for(int i=V.size(); i--;){
if(V.at(i) == b.V.at(i)) continue;
return V.at(i)>b.V.at(i);
}
return 2;
}
public:
bigint():isMinus(false),V({}){}
template<typename T>
bigint(T a){
if(a < 0) isMinus = true,a = -a;
else isMinus = false;
V = {};
while(a) V.push_back(a%10),a /= 10;
}
bigint(const string &s){
V = {};
if(s.size() == 0) isMinus = false;
else{
if(s.at(0) == '-') isMinus = true;
else isMinus = false;
for(int i=s.size(); i--;) V.push_back(s.at(i)-'0');
if(isMinus) V.pop_back();
while(V.size() && V.back() == '0') V.pop_back();
}
}
bigint(const bigint &n){isMinus = n.isMinus; V = n.V;}
bigint &operator=(const bigint &b) = default;
bigint operator+(const bigint &b){
bigint ret;
if(isMinus == b.isMinus){
ret = *this;
ret.V.resize(max(V.size(),b.V.size()));
for(int i=0; i<b.V.size(); i++) ret.V.at(i) += b.V.at(i);
}
else{
int now = comp(b);
if(now == 2) return bigint(0);
if(now == 1){
ret = *this;
for(int i=0; i<b.V.size(); i++) ret.V.at(i) -= b.V.at(i);
}
else{
ret = b;
for(int i=0; i<V.size(); i++) ret.V.at(i) -= V.at(i);
}
}
ret.slide(); return ret;
}
bigint operator-(const bigint &b){
bigint ret;
if(isMinus != b.isMinus){
ret = *this;
ret.V.resize(max(V.size(),b.V.size()));
for(int i=0; i<b.V.size(); i++) ret.V.at(i) += b.V.at(i);
}
else{
int now = comp(b);
if(now == 2) return bigint(0);
if(now == 1){
ret = *this;
for(int i=0; i<b.V.size(); i++) ret.V.at(i) -= b.V.at(i);
}
else{
ret = b; ret.isMinus ^= 1;
for(int i=0; i<V.size(); i++) ret.V.at(i) -= V.at(i);
}
}
ret.slide(); return ret;
}
bigint operator*(const bigint &b){
bigint ret; ret.isMinus = (isMinus^b.isMinus);
ret.V = convolution_int(V,b.V);
ret.slide(); return ret;
}
bigint operator/(const bigint &b){//b!=0.
assert(b.V.size());
bigint ret(0); ret.isMinus = isMinus^b.isMinus;
if(bigint(1) == b) return (*this);
if(b.V.size() < 64){
auto a = *this;
int n = (*this).V.size(),m = b.V.size();
for(int i=n-1; i>=0; i--){
int ok = 0;
bigint now;
for(int k=i; k<min(n,i+m+1); k++) now.V.push_back(a.V.at(k));
int memo = now.size();
while(now.V.size() && now.V.back() == 0) now.V.pop_back();
for(int v=1; v<10; v++){
if(now >= b) now -= b,ok++;
else break;
}
now.V.resize(memo);
for(int k=i; k<min(n,i+m+1); k++) a.V.at(k) = now.V.at(k-i);
ret.V.push_back(ok);
}
reverse(ret.V.begin(),ret.V.end());
while(ret.V.size() && ret.V.back() == 0) ret.V.pop_back();
return ret;
}
//ニュートン法.
int accu = 2,need = max(2,(int)V.size()-(int)b.V.size()+2);
bigint invB(10),two(200);
for(int i=0; i<6; i++){ //精度2桁までやる
bigint one = invB*b;
two.V.pop_back();
while(two.V.size() < one.V.size()) two.V.push_back(0);
while(two.V.size() > one.V.size()) two.V.pop_back();
two.V.push_back(2);
bigint next = invB*(two-one);
invB.V.assign(2,0);
invB.V.at(1) = next.V.back(); next.V.pop_back();
invB.V.at(0) = next.V.back();
}
while(accu < need){ //精度倍々になる.
bigint one = invB*b;
two.V.pop_back();
while(two.V.size() < one.V.size()) two.V.push_back(0);
two.V.push_back(2);
bigint next = invB*(two-one);
accu = min(accu<<1,need);
invB.V.clear();
for(int i=max(0,(int)next.V.size()-accu); i<next.V.size(); i++) invB.V.push_back(next.V.at(i));
}
{ //精度足りてない場合があるのでラスト1回.
bigint one = invB*b;
two.V.pop_back();
while(two.V.size() < one.V.size()) two.V.push_back(0);
two.V.push_back(2);
bigint next = invB*(two-one);
accu = min(accu<<1,need);
invB.V.clear();
for(int i=max(0,(int)next.V.size()-accu); i<next.V.size(); i++) invB.V.push_back(next.V.at(i));
}
bigint check = (*this)*invB; //floor(check)=ret.
for(int i=invB.V.size()+b.V.size()-1; i<check.V.size(); i++) ret.V.push_back(check.V.at(i));
if((*this)-ret*b >= b){ //+1の可能性.
int digit = 0;
ret.V.push_back(0);
ret.V.at(digit)++;
while(ret.V.at(digit) == 10) ret.V.at(digit) = 0,ret.V.at(++digit)++;
if(ret.V.back() == 0) ret.V.pop_back();
}
return ret;
}
bigint operator%(const bigint &b){ //a>=0,b>0を仮定.
bigint ret = *this;
ret -= ret/b*b;
return ret;
}
bigint operator+=(const bigint &b){return *this=*this+b;}
bigint operator-=(const bigint &b){return *this=*this-b;}
bigint operator*=(const bigint &b){return *this=*this*b;}
bigint operator/=(const bigint &b){return *this=*this/b;}
bigint operator%=(const bigint &b){return *this=*this%b;}
bool operator==(const bigint &b){
if(V.size() != b.V.size() || isMinus != b.isMinus) return false;
return V == b.V;
}
bool operator<(const bigint &b){
if(isMinus && !b.isMinus) return true;
if(!isMinus && b.isMinus) return false;
if(!isMinus && !b.isMinus){
if(V.size() < b.V.size()) return true;
if(V.size() > b.V.size()) return false;
for(int i=V.size(); i--;){
if(V.at(i) == b.V.at(i)) continue;
return V.at(i) < b.V.at(i);
}
return false;
}
else{
if(V.size() > b.V.size()) return true;
if(V.size() < b.V.size()) return false;
for(int i=V.size(); i--;){
if(V.at(i) == b.V.at(i)) continue;
return V.at(i) > b.V.at(i);
}
return false;
}
}
bool operator<=(const bigint &b){
if(isMinus && !b.isMinus) return true;
if(!isMinus && b.isMinus) return false;
if(!isMinus && !b.isMinus){
if(V.size() < b.V.size()) return true;
if(V.size() > b.V.size()) return false;
for(int i=V.size(); i--;){
if(V.at(i) == b.V.at(i)) continue;
return V.at(i) < b.V.at(i);
}
return true;
}
else{
if(V.size() > b.V.size()) return true;
if(V.size() < b.V.size()) return false;
for(int i=V.size(); i--;){
if(V.at(i) == b.V.at(i)) continue;
return V.at(i) > b.V.at(i);
}
return true;
}
}
bool operator>(const bigint &b){return !(*this<=b);}
bool operator>=(const bigint &b){return !(*this<b);}
bool operator!=(const bigint &b){return !(*this==b);}
unsigned int size(){return V.size();}
mint get(){
mint ret = 0,p10 = 1;
for(auto v : V) ret += p10*v,p10 *= 10;
return ret;
}
};
istream &operator>>(istream &is,bigint &a){
string s; cin >> s;
a = bigint(s);
return is;
}
ostream &operator<<(ostream &os,bigint a){
if(a.isMinus) cout << "-";
if(a.V.size() == 0) cout << 0;
for(int i=a.V.size(); i--;) cout << a.V.at(i);
return os;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
vector<vector<int>> all;
for(int i=2; i<=7; i++) for(int k=1; k<i; k++){
if(gcd(i,k) != 1) continue;
bool ok = true;
int s = 0;
vector<int> now;
for(int p=0; p<1000; p++){
s += k;
now.push_back(s>=i);
s %= i;
}
all.push_back(now);
}
for(int i=1; i<=1000; i++){
set<vector<int>> S;
for(auto &a : all){
S.insert(vector<int>(a.begin(),a.begin()+i));
}
break;
if(S.size() == all.size()){cout << i << endl; return 0;}
}
int T; cin >> T;
int Need = 100000;
vector<int> allp;
vector<bool> prime(Need+1,true);
prime.at(0) = false; prime.at(1) = false;
for(int i=2; i<=Need; i++){
if(!prime.at(i)) continue;
allp.push_back(i);
for(long long k=((long long)i)*i; k<=Need; k+=i) prime.at(k) = false;
}
while(T--){
bigint a,b,c; cin >> a >> b >> c;
mint answer = 0;
while(a%c == 0) answer += b.get(),a /= c;
long long a1 = 0,a2 = 0,a3 = 0,p15 = 1'000'000'000'000'000LL;
long long c1 = 0,c2 = 0,c3 = 0;
auto divA = [&](int p) -> void {
a /= p;
while(a.V.size() <= 40) a.V.push_back(0);
a1 = 0,a2 = 0,a3 = 0;
for(int i=14; i>=0; i--){
a1 *= 10,a1 += a.V.at(i);
}
for(int i=29; i>=15; i--){
a2 *= 10,a2 += a.V.at(i);
}
for(int i=40; i>=30; i--){
a3 *= 10,a3 += a.V.at(i);
}
while(a.V.back() == 0) a.V.pop_back();
};
auto divC = [&](int p) -> void {
c /= p;
while(c.V.size() <= 40) c.V.push_back(0);
c1 = 0,c2 = 0,c3 = 0;
for(int i=14; i>=0; i--){
c1 *= 10,c1 += c.V.at(i);
}
for(int i=29; i>=15; i--){
c2 *= 10,c2 += c.V.at(i);
}
for(int i=40; i>=30; i--){
c3 *= 10,c3 += c.V.at(i);
}
while(c.V.back() == 0) c.V.pop_back();
};
divA(1),divC(1);
pair<int,int> worst = {1,1};
auto chmin = [&](pair<int,int> check){if(worst.first*check.second > worst.second*check.first) worst = check;};
for(auto p : allp){
int one = 0,two = 0;
while((a1%p+a2%p*(p15%p)+a3%p*(p15%p)*(p15%p))%p == 0) divA(p),one++;
while((c1%p+c2%p*(p15%p)+c3%p*(p15%p)*(p15%p))%p == 0) divC(p),two++;
if(two == 0) continue;
chmin({one,two});
if(one == 0) break;
}
if(worst.first != 0 && c != 1){
bigint a2 = 1;
vector<int> plus1;
for(int i=0; i<7; i++){
a2 *= a;
if(a2%c == 0) a2 /= c,plus1.push_back(1);
else plus1.push_back(0);
}
for(int i=1; i<=7; i++) for(int k=0; k<i; k++){
if(gcd(i,k) != 1) continue;
bool ok = true;
int s = 0;
for(int p=0; p<plus1.size(); p++){
s += k;
if((s>=i)!=plus1.at(p)) ok = false;
s %= i;
}
if(ok) chmin({k,i});
}
}
bigint b2 = b/worst.second*worst.first;
int bint = (b%worst.second).get().v;
answer += b2.get();
for(int i=1; ; i++){
if(i*worst.second <= bint*worst.first) answer++;
else break;
}
cout << answer.v << "\n";
}
}