Everyone knows there is a computer game names "hearth stone", recently xzz likes this game very much. If you want to win, you need both capacity and good luck.
There is a spell card names "Arcane Missiles", which can deal 3 damages randomly split among all enemies.
xzz have a "Arcane Missiles Plus" can deal n damage randomly split among all enemies. The enemy battle field have only two characters: the enemy hero and enemy minion.
Now we assume the enemy hero have infinite health, the enemy minion has m health.
xzz wants to know the probability of the "Arcane Missiles Plus" to kill the enemy minion (the minion has not more than 0 health after "Arcane Missiles Plus"), can you help him?
The first line of the input contains an integer T, the number of test cases. T test cases follow. (1 ≤ T ≤ 100000)
Each test case consists of a single line containing two integer n and m. (0 ≤ m ≤ n ≤ 1000)
For each test case, because the probability can be written as x / y, please output x * y^-1 mod 1000000007. .(y * y^-1 ≡ 1 mod 10^9 + 7)
2 3 3 2 1
125000001 750000006