Bobo has a string of length 2 which consists of characters `A` and `B`. The string also has a fascinating property: it can be decomposed into subsequences of length 2, and among the subsequences n of them are `AB` while other m of them are `BA`. Given n and m, find the number of possible strings modulo .
Bobo has a string of length 2(n + m) which consists of characters `A` and `B`. The string also has a fascinating property: it can be decomposed into (n + m) subsequences of length 2, and among the (n + m) subsequences n of them are `AB` while other m of them are `BA`. Given n and m, find the number of possible strings modulo (109+7)(10^9+7)(109+7).
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