Consider a two player game where each player has $n$ cards numbered $1,2,\dots,n$ . On each turn both players place one of their cards on the table. The player who placed the higher card gets one point. If the cards are equal, neither player gets a point. The game continues until all cards have been played.
You are given the number of cards $n$ and the players' scores at the end of the game, $a$ and $b$ . Your task is to count the number of possible games with that outcome.
The first line contains one integer $t$ : the number of tests.
Then there are $t$ lines, each with three integers $n$ , $a$ and $b$ .
For each test case print the number of possible games modulo $10^9+7$ .
5 3 1 2 2 0 1 5 2 2 9 3 5 4 4 1\n · · \n · · \n · · \n · · \n · · \n
6 0 4200 976757050 0\n \n \n \n \n