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.