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: Wrong Answer)

#include<bits/stdc++.h>
#include<regex>
#include<cctype>
using namespace std;
#define INFS (1LL<<28)
#define INF (1LL<<60)
#define DEKAI 1000000007
#define MOD 1000000007
#define lp(i,n) for(int i=0;i<n;i++)
#define double long double
#define all(c) begin(c), end(c)

#define int long long 

namespace {
#define __DECLARE__(C)    \
    template <typename T> \
    std::ostream &operator<<(std::ostream &, const C<T> &);

#define __DECLAREM__(C)               \
    template <typename T, typename U> \
    std::ostream &operator<<(std::ostream &, const C<T, U> &);

__DECLARE__(std::vector)
__DECLARE__(std::deque)
__DECLARE__(std::set)
__DECLARE__(std::stack)
__DECLARE__(std::queue)
__DECLARE__(std::priority_queue)
__DECLARE__(std::unordered_set)
__DECLAREM__(std::map)
__DECLAREM__(std::unordered_map)

template <typename T, typename U>
std::ostream &operator<<(std::ostream &, const std::pair<T, U> &);
template <typename... T>
std::ostream &operator<<(std::ostream &, const std::tuple<T...> &);
template <typename T, std::size_t N>
std::ostream &operator<<(std::ostream &, const std::array<T, N> &);

template <typename Tuple, std::size_t N>
struct __TuplePrinter__ {
    static void print(std::ostream &os, const Tuple &t) {
        __TuplePrinter__<Tuple, N - 1>::print(os, t);
        os << ", " << std::get<N - 1>(t);
    }
};

template <typename Tuple>
struct __TuplePrinter__<Tuple, 1> {
    static void print(std::ostream &os, const Tuple &t) { os << std::get<0>(t); }
};

template <typename... T>
std::ostream &operator<<(std::ostream &os, const std::tuple<T...> &t) {
    os << '(';
    __TuplePrinter__<decltype(t), sizeof...(T)>::print(os, t);
    os << ')';
    return os;
}

template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &v) {
    return os << '(' << v.first << ", " << v.second << ')';
}

#define __INNER__                             \
    os << '[';                                \
    for (auto it = begin(c); it != end(c);) { \
        os << *it;                            \
        os << (++it != end(c) ? ", " : "");   \
    }                                         \
    return os << ']';

template <typename T, std::size_t N>
std::ostream &operator<<(std::ostream &os, const std::array<T, N> &c) {
    __INNER__
}

#define __DEFINE__(C)                                           \
    template <typename T>                                       \
    std::ostream &operator<<(std::ostream &os, const C<T> &c) { \
        __INNER__                                               \
    }

#define __DEFINEM__(C)                                             \
    template <typename T, typename U>                              \
    std::ostream &operator<<(std::ostream &os, const C<T, U> &c) { \
        __INNER__                                                  \
    }

#define __DEFINEW__(C, M1, M2)                                  \
    template <typename T>                                       \
    std::ostream &operator<<(std::ostream &os, const C<T> &c) { \
        std::deque<T> v;                                        \
        for (auto d = c; !d.empty(); d.pop()) v.M1(d.M2());     \
        return os << v;                                         \
    }

__DEFINE__(std::vector)
__DEFINE__(std::deque)
__DEFINE__(std::set)
__DEFINEW__(std::stack, push_front, top)
__DEFINEW__(std::queue, push_back, front)
__DEFINEW__(std::priority_queue, push_front, top)
__DEFINE__(std::unordered_set)
__DEFINEM__(std::map)
__DEFINEM__(std::unordered_map)
}


#define rep(i,n) lp(i,n)
using Weight = int;
using Flow = int;
struct Edge {
    int src, dst;
    Weight weight;
    Flow cap;
    Edge() : src(0), dst(0), weight(0) {}
    Edge(int s, int d, Weight w) : src(s), dst(d), weight(w) {}
};
using Edges = std::vector<Edge>;
using Graph = std::vector<Edges>;
using Array = std::vector<Weight>;
using Matrix = std::vector<Array>;

void add_edge(Graph &g, int a, int b, Weight w = 1) {
    g[a].emplace_back(a, b, w);
    g[b].emplace_back(b, a, w);
}
void add_arc(Graph &g, int a, int b, Weight w = 1) { g[a].emplace_back(a, b, w); }

#define ll long long
ll modpow(ll x, ll y) {
    if (y == 0) return 1;
    ll res = modpow(x, y / 2);
    return res * res % MOD * (y & 1 ? x : 1) % MOD;
}
ll modinv(ll x) { return modpow(x, MOD - 2); }

signed main(){
	int x,y;
	cin>>x>>y;
	int nowx=0,nowy=0;
	int up=-1,left=-1;
	lp(i,2000000){
		int cx=x-nowx;
		int cy=y-nowy;
		if(cx<0||cy<0){
			cout<<0<<endl;
			return 0;
		}
		if(cy%2==0){
			if(cx==cy/2){
				left=i;
				up=cx;
				break;
			}
		}
		nowx+=2;
		nowy+=1;
	}
	cout<<up<<left<<endl;
	int ue=1,down=1;
	lp(i,left){
		down*=(i+1);
		down%=MOD;
	}
	lp(i,up){
		down*=(i+1);
		down%=MOD;
	}
	lp(i,up+left){
		ue*=(i+1);
		ue%=MOD;
	}
	cout<<ue*modinv(down)%MOD<<endl;
	return 0;
}