假如把A看成1，B看成-1。根据它的条件会发现，他们的前缀和满足一个规律：[-m, n]。然后枚举每个位置。
可以看作是直角坐标系，原点为0。
x轴正方向看作A的数量，值为左边位置的值+1，当超出范围时置为0。
y轴正方向看作B的数量，值为下边位置的值-1，当超出范围时置为0.
其他位置均只能从左侧或下侧走到，即值为左侧加下侧的总和，当超出范围时置为0.
Code
/**
* author: Akvicor
* created: 2019-07-21 09-37-22
**/
#include <bits/stdc++.h>
using namespace std;
#ifdef DEBUG
#define FAST_IO 17
#else
#define FAST_IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define endl '\n'
#endif
#define rep(i, n) for(int i = 0; i < (n); ++i)
#define reep(i, n) for(int i = 0; i <= (n); ++i)
#define lop(i, a, n) for(int i = a; i < (n); ++i)
#define loop(i, a, n) for(int i = a; i <= (n); ++i)
#define prec(x) fixed << setprecision(x)
#define ms(s, n) memset(s, n, sizeof(s))
#define all(v) (v).begin(), (v).end()
#define sz(x) ((int)(x).size())
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define MOD(x) const int MOD = (int)x + 7
#define MAXN(x) const int MAXN = (int)x + 7
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<PII> VII;
namespace SOL{
const double EPS = 1e-6;
const double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
const LL LINF = 0x7f7f7f7f7f7f7f7f;
/** >------- Akvicor's Solution -------< **/
MOD(1e9);
MAXN(1e6);
void mod(long long & n){ n %= (long long)MOD; }
void mod(int & n){ n %= MOD; }
LL dp[3010][3010];
void solve(){
FAST_IO;
int n, m;
while(cin >> n >> m){
reep(i, n+m) reep(j, n+m) dp[i][j] = 0;
dp[0][0] = 1;
reep(i, n+m) reep(j, n+m){
if(i) dp[i][j] += dp[i-1][j];
if(j) dp[i][j] += dp[i][j-1];
//dp[i][j] %= MOD;
mod(dp[i][j]);
if(i-j > n || j-i > m) dp[i][j] = 0;
}
cout << dp[n+m][n+m] << endl;
}
}
/** >----------------------------------< **/
}
int main(){
#ifdef DEBUG
int DEBUGCNT = 0;
clock_t DEBUGstart, DEBUGfinish;
double DEBUGduration;
cout << ">------- Akvicor's Solution -------<" << endl;
DEBUGLOOP:
DEBUGstart = clock();
#endif
SOL::solve();
#ifdef DEBUG
DEBUGfinish = clock();
DEBUGduration = (double)(DEBUGfinish - DEBUGstart)*1000 / CLOCKS_PER_SEC;
if(DEBUGduration > 0.07)
cout << " --> Test: #" << DEBUGCNT << " time: " << fixed << setprecision(4) << DEBUGduration << " ms <--" << endl;
++DEBUGCNT;
if(DEBUGCNT < 100) goto DEBUGLOOP;
cout << ">----------------------------------<" << endl;
#endif
return 0;
}