test/yuki4459.test.cpp

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Last update: 2023-04-05 23:10:22+09:00
Problem: https://yukicoder.me/problems/4459

Depends on

Code

#define PROBLEM "https://yukicoder.me/problems/4459"

#include "../template.hpp"

#include "../Math/ceil_floor.hpp"


template< typename T >
inline T extgcd(T a, T b, T &x, T &y) {
  T d = a;
  if(b != 0) {
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  } else {
    x = 1;
    y = 0;
  }
  return d;
}

vector<ll> ve(3);

void solve(){
    cin>>ve;
    ll y;cin>>y;
    sort(ALL(ve));
    ll a,b,c;
    a=ve[2],b=ve[1],c=ve[0];

    ll res=0;

    ll g=gcd(b,c);
    ll j,k;
    ll u=b/g,v=c/g;

    ll gg=extgcd(u,v,j,k);


    for(ll i=0;i<=y;i+=a){
        ll t=y-i;
        if(t%g) continue;
        t/=g;

        ll w=t/gg; // t=g*w
        
        // g=j*u+k*v;
        ll jj=j*w,kk=k*w;

        // j=j' + x * v
        // k=k' - x * u

        jj*=-1;
        ll dw=div_ceil(jj,v);
        ll up=div_floor(kk,u);
        // cout<<up<<" ~ "<<dw<<endl;
        res+=max(0ll,(up-dw+1));
        if(res>=mod) res%=1000000007ll;
    }
    cout<<res<<"\n";
}


signed main(){
    int q;cin>>q;
    while(q--) solve();
    return 0;
}

#line 1 "test/yuki4459.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/4459"

#line 1 "template.hpp"
#include<bits/stdc++.h>
using namespace std;
#define ALL(x) begin(x),end(x)
#define rep(i,n) for(int i=0;i<(n);i++)
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define mod 1000000007
using ll=long long;
const int INF=1000000000;
const ll LINF=1001002003004005006ll;
int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
// ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}

struct IOSetup{
    IOSetup(){
        cin.tie(0);
        ios::sync_with_stdio(0);
        cout<<fixed<<setprecision(12);
    }
} iosetup;
 
template<typename T>
ostream &operator<<(ostream &os,const vector<T>&v){
    for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" ");
    return os;
}
template<typename T>
istream &operator>>(istream &is,vector<T>&v){
    for(T &x:v)is>>x;
    return is;
}

#line 4 "test/yuki4459.test.cpp"

#line 1 "Math/ceil_floor.hpp"
// round for +inf
template<typename INT>
inline INT div_ceil(INT x,INT y){
    return (x<0?x/y:(x+y-1)/y);
}

// round for -inf
template<typename INT>
inline INT div_floor(INT x,INT y){
    return (x>0?x/y:(x-y+1)/y);
}
#line 6 "test/yuki4459.test.cpp"


template< typename T >
inline T extgcd(T a, T b, T &x, T &y) {
  T d = a;
  if(b != 0) {
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  } else {
    x = 1;
    y = 0;
  }
  return d;
}

vector<ll> ve(3);

void solve(){
    cin>>ve;
    ll y;cin>>y;
    sort(ALL(ve));
    ll a,b,c;
    a=ve[2],b=ve[1],c=ve[0];

    ll res=0;

    ll g=gcd(b,c);
    ll j,k;
    ll u=b/g,v=c/g;

    ll gg=extgcd(u,v,j,k);


    for(ll i=0;i<=y;i+=a){
        ll t=y-i;
        if(t%g) continue;
        t/=g;

        ll w=t/gg; // t=g*w
        
        // g=j*u+k*v;
        ll jj=j*w,kk=k*w;

        // j=j' + x * v
        // k=k' - x * u

        jj*=-1;
        ll dw=div_ceil(jj,v);
        ll up=div_floor(kk,u);
        // cout<<up<<" ~ "<<dw<<endl;
        res+=max(0ll,(up-dw+1));
        if(res>=mod) res%=1000000007ll;
    }
    cout<<res<<"\n";
}


signed main(){
    int q;cin>>q;
    while(q--) solve();
    return 0;
}