Problem:
Score : 400 points

Problem Statement

There is a knight - the chess piece - at the origin (0, 0) of a two-dimensional grid.

When the knight is at the square (i, j), it can be moved to either (i+1,j+2) or (i+2, j+1).

In how many ways can the knight reach the square (X, Y)?

Find the number of ways modulo 10^9 + 7.

Constraints

1 \leq X \leq 10^6

1 \leq Y \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

Print the number of ways for the knight to reach (X, Y) from (0, 0), modulo 10^9 + 7.

Sample Input 1

3 3

Sample Output 1

2

There are two ways: (0,0) \to (1,2) \to (3,3) and (0,0) \to (2,1) \to (3,3).

Sample Input 2

2 2

Sample Output 2

0

The knight cannot reach (2,2).

Sample Input 3

999999 999999

Sample Output 3

151840682

Print the number of ways modulo 10^9 + 7.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define int long long
#define double long double
#define fo(a,b) for(int a=0;a<b;a++)
#define Sort(a) sort(a.begin(),a.end())
#define rev(a) reverse(a.begin(),a.end())
#define fi first
#define se second
#define co(a) cout<<a<<endl
#define sz size()
#define bgn begin()
#define en end()
#define pb(a) push_back(a)
#define pp() pop_back()
#define V vector
#define P pair
#define V2(a,b,c) V<V<int>> a(b,V<int>(c))
#define V2a(a,b,c,d) V<V<int>> a(b,V<int>(c,d))
#define incin(a) int a; cin>>a
#define yuko(a) setprecision(a)
#define uni(a) a.erase(unique(a.begin(),a.end()),a.end())
#define pri priority_queue
#define Pri priority_queue<int,vector<int>,greater<int>>
#define ff fi.fi
#define fs fi.se
#define sf se.fi
#define ss se.se
#define all(a)  (a).begin(),(a).end()
#define Pi P<int,int>
#define elif else if
//#define min min<int>
//#define max max<int>
int low(V<int> a,int b){
  decltype(a)::iterator c=lower_bound(a.begin(),a.end(),b);
  int d=c-a.bgn;
  return d;
}
int upp(V<int> a,int b){
  decltype(a)::iterator c=upper_bound(a.begin(),a.end(),b);
  int d=c-a.bgn;
  return d;
}
template<class T>
 void cou(vector<vector<T>> a){
  int b=a.size();
  int c=a[0].size();
  fo(i,b){
    fo(j,c){
      cout<<a[i][j];
      if(j==c-1)
        cout<<endl;
      else
        cout<<' ';
    }
  }
}
/*template<>
 void cou(vector<vector<char>> a){
  int b=a.size();
  int c=a[0].size();
  fo(i,b){
    fo(j,c){
      cout<<a[i][j];
      if(j==c-1)
        cout<<endl;
      else
        cout<<' ';
    }
  }
}*/
 int wari(int a,int b) {
   if(a%b==0)
     return a/b;
   else
     return a/b+1;
 }
 int keta(int a){
  double b=a;
  b=log10(b);
  int c=b;
  return c+1;
 }
 int souwa(int a){
  return a*(a+1)/2;
 }
 /*int lcm(int a,int b){
  int d=a,e=b,f;
  if(a<b)
    swap(a,b);
  int c,m=1;
  while(m){
    c=a%b;
    if(c==0){
       f=b;
      m--;
    }
    else{
      a=b;
      b=c;
 }
  }
  return d*e/f;
    } */
int gcm(int a,int b){
  if(a%b==0)
    return b;
  return gcm(b,a%b);
}
 bool prime(int a){
   if(a<2)
     return false;
   else if(a==2)
     return true;
   else if(a%2==0)
     return false;
   double b=sqrt(a);
    for(int i=3;i<=b;i+=2){
      if(a%i==0){
        return false;
      }
    }
   return true;
 }

struct Union{
  vector<int> par;
  Union(int a){
  par= vector<int>(a,-1);
  }
  int find(int a){
    if(par[a]<0)
      return a;
    else
      return par[a]=find(par[a]);
  }
  bool same(int a,int b){
    return find(a)==find(b);
  }
  int Size(int a){
    return -par[find(a)];
  }
  void unite(int a,int b){
    a=find(a);
    b=find(b);
    if(a==b)
      return;
    if(Size(b)>Size(a))
      swap<int>(a,b);
    par[a]+=par[b];
    par[b]=a;
  }
};
int ketas(int a){
  string b=to_string(a);
  int c=0;
  fo(i,keta(a)){
    c+=b[i]-'0';
  }
  return c;
}
/*int gcm(int a,int b){
    if(b==0)
        return a;
    return gcm(b,a%b);
}*/
int lcm(int a,int b){
    return a/gcm(a,b)*b;
}
/*struct aa{
  vector<int> gt;
  aa(int n){
  gt= vector<int>(n, 1);
  }
  void c(V<int> d,int b){
  if(d[b]==0){
    gt[d[b]-1]++;
    gt[gt.sz-1]++;
  }
  else{
    gt[d[b]-1]++;
    c(d,d[d[b]]-1);
  }
}
void cok(int a){
  cout<<gt[a-1]<<endl;
  fo(i,a-1)
  cout<<gt[i]<<endl;
}
};
*/
/*struct dfs(){

}*/
bool fe(int a,int b){
  a%=10;
  b%=10;
  if(a==0)
    a=10;
  if(b==0)
    b=10;
  if(a>b)
    return true;
  else
    return false;
}
int INF=1000000007;
struct edge{int s,t,d; };
V<int> mojisyu(string a){
  V<int> b(26,0);
  fo(i,a.sz){
    b[a[i]-'a']++;
  }
  return b;
}
int wa2(int a){
  if(a%2==1)
    return a/2;
  return a/2-1;
}
/*signed main(){
  int a,b,c;
  cin>>a>>b>>c;
  V<V<edge>> d(a);
  fo(i,b){
    edge e;
    cin>>e.s>>e.t>>e.d;
    d[e.s].pb(e);
  }
  V<int> e(a,INF);
  e[c]=0;
  priority_queue<P<int,int>,V<P<int,int>>,greater<P<int,int>>> f;
  f.push({0,c});
  int h=INF;
  while(!f.empty()){
    P<int,int> g;
    g=f.top();
    f.pop();
    int v = g.second, i = g.first;
    for(edge l : d[v]){
      if(e[l.t] > i + l.d){
        e[l.t] = i + l.d;
        f.push({i+l.d , l.t});
      }
    }
  }
  fo(i,a){
    if(e[i]==INF)
      cout<<"INF"<<endl;
    else
      cout<<e[i]<<endl;
  }
}
?*/
int nCr(int n,int r){
  int a=1;
  r=min(r,n-r);
  for(int i=n;i>n-r;i--){
    a*=i;
    a/=n-i+1;
  }
  return a;
}

int a,b,e=0;
V<V<char>> c(55,V<char>(55));
V<V<int>> d(55,V<int>(55,0));
void sea(int x,int y){
  if(x<0||a<=x||y<0||b<=y||c[x][y]=='#')
    return;
  if(d[x][y])
    return;
  d[x][y]++;
  sea(x+1,y);
  sea(x-1,y);
  sea(x,y+1);
  sea(x,y-1);
}
int kaijou(int a){
  int b=1;
  fo(i,a)
    b*=i+1;
  return b;
}
int nPr(int a,int b){
  int c=1;
  for(int i=a;i>=b;i--)
    c*=i;
  return c;
}
V<V<int>> comb(int n,int r){
  V<V<int>> v(n+1,V<int>(n+1,0));
  for(int i=0;i<v.sz;i++) {
    v[i][0]=1;
    v[i][i]=1;
  }
  for(int j=1;j<v.sz;j++){
    for(int k=1;k<j;k++){
      v[j][k]=(v[j-1][k-1]+v[j-1][k])%INF;
    }
  }
  return v;
}
int ncr(int n,int r){
        int num=1;
        for(int i=1;i<=r;i++){
            num=(num*(n-i+1)/i)%INF;
        }
        return num;
    }
int combination(int n, int r)
{
    if (r == 0 || r == n)
        return (1);
    else if (r == 1)
        return (n);
    return (combination(n - 1, r - 1)%INF + combination(n - 1, r))%INF;
}
int combinations2(int n,int k) {
    int r = 1;
    for (int d = 1; d <= k; ++d) {
        r *= n;
      n--;
        r /= d;
      r%=INF;
    }
    return r;
}
int MOD=INF;
int fac[1000010], finv[1000010], inv[1000010];
 
// テーブルを作る前処理
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < 1000010; i++){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}
 
// 二項係数計算
long long COM(int n, int k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
 
signed main(){
  int a,b;
  cin>>a>>b;
  int c=1;
  if((a+b)%3!=0)
    c=0;
  if(a>b)
    swap(a,b);
  int d=b-a;
  if(d>a||(a-d)%3!=0)
    c=0;
  
  if(c){
    int e=d+(a-d)/3*2;
    int f=(a-d)/3;
    e%=INF;
    f%=INF;
/*    cout<<e<<' '<<f<<endl;
    cout<<combinations2(e,f)<<endl;*/
    COMinit();
    cout<<COM(e,f)<<endl;
  }
  else
    cout<<0<<endl;
}