Your task is to calculate $n$ binomial coefficients modulo $10^9+7$.

A binomial coefficient ${a \choose b}$ can be calculated using the formula $\frac{a!}{b!(a-b)!}$. We assume that $a$ and $b$ are integers and $0 \le b \le a$.

Input

The first input line contains an integer $n$: the number of calculations.

After this, there are $n$ lines, each of which contains two integers $a$ and $b$.

Output

Print each binomial coefficient modulo $10^9+7$.

Constraints

• $1 \le n \le 10^5$
• $0 \le b \le a \le 10^6$

Example

Input:

3
5 3
8 1
9 5

Output:

10
8
126