You are given a $$2-D$$ matrix of length $$n$$ and width $$m$$. There is exactly one blocked cell in a $$2D$$ matrix that is uniformly chosen among all points except $$(1,1)$$ and $$(n,m)$$.

Find the expected number of paths from $$(1,1)$$ to $$(n,m)$$. You can only move rightwards and downwards. If the expected number of paths is $$\frac{p}{q}$$ in the simplest form, then print $$(p.q^{-1})$$ modulo $$1000000007$$ where $$q^{-1}$$ is the multiplicative inverse of $$q$$ modulo $$1000000007$$.

Input format

Each test contains multiple test cases. The first line contains $$T$$ denoting the number of test cases. $$(1\leq T \leq100000)$$
The first and only line of each test case contains two space-separated integers $$n (2\leq n\leq100000)$$ and $$m (2\leq m\leq100000)$$ representing the length and the width of the $$2D$$ matrix respectively.

Output format

For each test case, print a single line containing one integer $$(p.q^{-1})$$ modulo $$1000000007$$ where $$\frac{p}{q}$$ is the expected number of paths.