For given integers $n$ and $m$, let's call a pair of arrays $a$ and $b$ of integers good, if they satisfy the following conditions:

• $a$ and $b$ have the same length, let their length be $k$.
• $k \ge 2$ and $a_1 = 0, a_k = n, b_1 = 0, b_k = m$.
• For each $1 < i \le k$ the following holds: $a_i \geq a_{i - 1}$, $b_i \geq b_{i - 1}$, and $a_i + b_i \neq a_{i - 1} + b_{i - 1}$.

Find the sum of $|a|$ over all good pairs of arrays $(a,b)$. Since the answer can be very large, output it modulo $10^9 + 7$.

The input consists of multiple test cases. The first line contains a single integer $t (1 \leq t \leq 10^4)$  — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $m$ $(1 \leq n, m \leq 5 \cdot 10^6)$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $5 \cdot 10^6$ and the sum of $m$ over all test cases does not exceed $5 \cdot 10^6$.

For each test case, output a single integer  — the sum of $|a|$ over all good pairs of arrays $(a,b)$ modulo $10^9 + 7$.