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++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
using lli = long long;
#define rep(i,n) for(int i=0;i<n;i++)
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }

#define N 6e6
const lli mod = 1e9+7;
lli x, y;
vector<lli> inv(N);
vector<lli> fact(N);
vector<lli> fact_inv(N);

void setinv(){
    inv[1] = 1;
    for(int i = 2; i < N; i++){
        inv[i] = mod-((mod/i)*inv[mod%i]%mod);
    }
}
void setfact(){
    fact[0] = fact[1] = 1;
    for(int i = 2; i < N; i++){
        fact[i] = i*fact[i-1]%mod;
    }
}
void setfact_inv(){
    fact_inv[0] = fact_inv[1] = 1;
    for(int i = 2; i < N; i++){
        fact_inv[i] = inv[i]*fact_inv[i-1]%mod;
    }
}
lli comb(lli n, lli k){
    lli ret = (fact[n]*fact_inv[k]%mod)*fact_inv[n-k]%mod;
    return ret;
}

int main(void){
    setinv();
    setfact();
    setfact_inv();
    cin >> x >> y;
    lli a = 2*y-x;
    lli b = 2*x-y;
    if(a%3 != 0 || b%3 != 0){
        cout << 0 << endl;
        return 0;
    }
    a/=3;
    b/=3;
    cout << comb(a+b, a) << endl;
    return 0;
}