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"
#define rep(i,n) for (int i=0; i<(n); ++i)
using namespace std;
using ll =long long;
using P =pair<int,int>;


    ll nck(ll n, ll k){
    
    ll p=1000000007;
    ll p2;
    p2=p-2;
    vector <int> r(35);
    vector <ll> r2(36);

    rep(j,35){
        r[j]=(p2>>j)&1;
    }

    ll ans;
    ans=1;

    if (k!=0){
    rep(i,k-1){
        
        
        r2[0]=i+2;
        rep(j,35){
           
            r2[j+1]=(r2[j]*r2[j])%p;
            if(r[j]==1){
            ans*=r2[j];
            ans=ans%p;
            }
        }
    }
    

   

    rep(i,k){
        ans*=n-i;
        ans=ans%p;
    }
    }
    


    return ans;
}




int main(){
    ll x,y,a,b;
    cin >> x >> y;
    int k;
    k=0;
    if((2*y-x)%3!=0 or (2*x-y)%3!=0){
        k=1;
    }
    ll m;
    a=2*y-x;
    b=2*x-y;

    if(a<0 or b<0){
        k=2;
    }
    a/=3;
    b/=3;
    m=min(a,b);
    

    ll ans;
    
    if(k==0){
        ans=nck(a+b,m);
    }
    if(k==1 or k==2){
        cout << 0 << endl;
    }
    else{
    cout << ans << endl;
    }
    return 0;
}